Analysis

Author

ak

#Load libraries
library(tidyverse)
── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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✔ ggplot2   3.4.4     ✔ tibble    3.2.1
✔ lubridate 1.9.3     ✔ tidyr     1.3.0
✔ purrr     1.0.2     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(lme4)
Warning: package 'lme4' was built under R version 4.3.2
Loading required package: Matrix
Warning: package 'Matrix' was built under R version 4.3.2

Attaching package: 'Matrix'

The following objects are masked from 'package:tidyr':

    expand, pack, unpack
library(ggfortify)
Warning: package 'ggfortify' was built under R version 4.3.2
library(lmerTest)
Warning: package 'lmerTest' was built under R version 4.3.2

Attaching package: 'lmerTest'

The following object is masked from 'package:lme4':

    lmer

The following object is masked from 'package:stats':

    step
library(performance)
Warning: package 'performance' was built under R version 4.3.2
library(readr)
#install.packages("broom.mixed")
library(broom.mixed)
Warning: package 'broom.mixed' was built under R version 4.3.2
library(grid)

Load data

droughtnet <- read_csv("droughtnet_data_cleaned_final.csv", 
                 col_types = cols(calluna_shoot_type = col_factor(levels = c("Long", "Short"))),
                 guess_max = Inf)

View(droughtnet)
# Specify the columns to check for NA values
# List of columns to check for NA values
columns_to_check <- c("DroughtTrt", "DroughNet_plotID", "ageClass", "siteID", 
                      "species", "plant_height", "SLA", "mean_thickness", "dry_mass_g_original", "LDMC", "leaf_area", "wet_mass_g", "dry_mass_g")


# Check for rows with any NA values in the specified columns
na_rows <- apply(droughtnet[columns_to_check], 1, function(row) any(is.na(row)))

# Create a data frame showing how many NA values there are in each row
na_row_summary <- droughtnet[na_rows, columns_to_check]
na_row_summary$row_na_count <- rowSums(is.na(na_row_summary))

# Summarize the number of rows by the count of NAs they contain
na_row_summary <- na_row_summary %>%
  group_by(row_na_count) %>%
  summarise(n = n(), .groups = 'drop')

# Create a summary showing the co-occurrence of NA values across the specified columns
na_co_occurrence <- droughtnet %>%
  summarise(across(all_of(columns_to_check), ~ sum(is.na(.)))) %>%
  pivot_longer(cols = everything(), names_to = "variable", values_to = "na_count") %>%
  arrange(desc(na_count))

# Print the summaries
print(paste("Total rows with any NA values across checked columns:", sum(na_rows)))
[1] "Total rows with any NA values across checked columns: 50"
print(na_row_summary)
# A tibble: 4 × 2
  row_na_count     n
         <dbl> <int>
1            1     9
2            2    32
3            4     2
4            5     7
print(na_co_occurrence)
# A tibble: 13 × 2
   variable            na_count
   <chr>                  <int>
 1 SLA                       37
 2 leaf_area                 36
 3 LDMC                      13
 4 wet_mass_g                12
 5 plant_height               9
 6 dry_mass_g                 8
 7 dry_mass_g_original        1
 8 DroughtTrt                 0
 9 DroughNet_plotID           0
10 ageClass                   0
11 siteID                     0
12 species                    0
13 mean_thickness             0
# Create the new data frame with selected columns
droughtnet_data2 <- select(droughtnet, 
                           "envelope_ID", "siteID", "species", "ageClass", "DroughtTrt", 
                           "DroughNet_plotID", "leaf_age", "calluna_shoot_type", 
                           "plant_height", "mean_thickness", "SLA", "LDMC", "plant_nr")

view(droughtnet_data2)

# Specify the columns to check for NA values
columns_to_check <- c("plant_height", "mean_thickness", "SLA", "LDMC")

# Remove rows with any NA values in the specified columns
droughtnet_data2_clean <- droughtnet_data2[!rowSums(is.na(droughtnet_data2[columns_to_check])), ]
view(droughtnet_data2_clean)
# Calculate the total number of NAs removed (for the specified columns only)
# This calculation considers rows removed rather than individual NAs
total_NAs_removed <- nrow(droughtnet_data2) - nrow(droughtnet_data2_clean)

# Calculate the total number of entries remaining
total_entries_remaining <- nrow(droughtnet_data2_clean)

# Print out the total NAs removed and total entries remaining
cat("Total NAs removed:", total_NAs_removed, "\n")
Total NAs removed: 50 
cat("Total entries remaining:", total_entries_remaining, "\n")
Total entries remaining: 1265 

Analysis of young leaves for the four focal species

# Specify the species of interest, including Calluna vulgaris
species_of_interest <- c("Empetrum nigrum", "Vaccinium myrtillus", "Vaccinium vitis-idaea", "Calluna vulgaris")

# Filter the data to include only the specified species where leaf_age is 'young',
# and for Calluna vulgaris, additionally check that calluna_shoot_type is 'short'

filtered_data <- droughtnet_data2_clean %>%
  filter(species %in% species_of_interest, leaf_age == "young") %>%
  filter(
    # Include Calluna vulgaris from Tjøtta regardless of calluna_shoot_type
    (species == "Calluna vulgaris" & siteID == "Tjøtta") |
    # Include Calluna vulgaris from Lygra only if calluna_shoot_type is Short
    (species == "Calluna vulgaris" & siteID == "Lygra" & calluna_shoot_type == "Short") |
    # Include other species of interest from both sites
    (species != "Calluna vulgaris")
  )

view(filtered_data)

D. plots for young leaves for the traits

filtered_data  <- filtered_data  %>%
  filter(siteID %in% c("Tjøtta", "Lygra"),
         DroughtTrt %in% c("Amb (0)", "Ext (90)"),
         ageClass %in% c("Pioneer", "Mature"))

ggplot(filtered_data, aes(x = species, y = plant_height, fill = DroughtTrt)) +
  geom_boxplot() +
  facet_grid(ageClass ~ siteID, scales = "free") +  # Removed leaf_age from facet_grid
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  labs(title = "Plant Height vs Treatment by Species for Young Leaves",
       x = "Species",
       y = "Plant Height") +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))  # Assigning colors to treatments

ggplot(filtered_data, aes(x = species, y = log(SLA), fill = DroughtTrt)) +
  geom_boxplot() +
  facet_grid(ageClass ~ siteID, scales = "free") + 
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1), # vertical adjustment for x axis labels
        plot.caption = element_text(hjust = 0.5)) + # Center the caption
  labs(title = "SLA vs Treatment by Species",
       x = "Species",
       y = "Log (SLA)",
       fill = "Drought Treatment",
       caption = "Figure 2: SLA Variation in Dwarf Shrubs Under Drought Conditions Across Different Ages and Sites") +
  scale_fill_manual(values = c("Amb (0)" = "orange", "Ext (90)" = "darkgrey")) # Assigning colors to treatments

ggplot(filtered_data, aes(x = species, y = LDMC, fill = DroughtTrt)) +
  geom_boxplot() +
  facet_grid(ageClass ~ siteID, scales = "free") + 
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1), # vertical adjustment for x axis labels
        plot.caption = element_text(hjust = 0.5)) + # Center the caption
  labs(title = "LDMC vs Treatment by Species",
       x = "Species",
       y = "LDMC",
       fill = "Drought Treatment",
       caption = "Figure 3: LDMC Variation in dwarf Shrubs Under drought conditions across different successional phases and sites") +
  scale_fill_manual(values = c("Amb (0)" = "darkblue", "Ext (90)" = "lightblue")) # Assigning colors to treatments

filtered_data  <- filtered_data  %>%
  filter(siteID %in% c("Tjøtta", "Lygra"),
         DroughtTrt %in% c("Amb (0)", "Ext (90)"),
         ageClass %in% c("Pioneer", "Mature"))

ggplot(filtered_data, aes(x = species, y = mean_thickness, fill = DroughtTrt)) +
  geom_boxplot() +
  facet_grid(ageClass ~ siteID, scales = "free") +  # Removed leaf_age from facet_grid
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  labs(title = "Plant Height vs Treatment by Species for Young Leaves",
       x = "Species",
       y = "mean_thickness") +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))  # Assigning colors to treatments

Trait 1- LDMC- models

# fitting a linear mixed-effects model using lmer, plant nr is the nested random effect
# Ensure variables are treated as categorical if they represent categories
filtered_data$DroughNet_plotID <- as.factor(filtered_data$DroughNet_plotID)

# Model with all the main effects for LDMC
model_main_effects_LDMC <- lmer(LDMC ~ species + DroughtTrt + ageClass + siteID +
                                (1 | DroughNet_plotID/plant_nr),
                                data = filtered_data)

summary(model_main_effects_LDMC)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: 
LDMC ~ species + DroughtTrt + ageClass + siteID + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 8228.9

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.7757 -0.5602  0.0437  0.5846  5.7000 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept)  300.3   17.33   
 DroughNet_plotID          (Intercept)  171.6   13.10   
 Residual                              2643.3   51.41   
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                             Estimate Std. Error      df t value Pr(>|t|)    
(Intercept)                   349.198      8.257  26.279  42.292  < 2e-16 ***
speciesEmpetrum nigrum          8.147      5.276 721.162   1.544 0.122988    
speciesVaccinium myrtillus      2.088      5.481 700.600   0.381 0.703352    
speciesVaccinium vitis-idaea  -21.253      5.136 690.820  -4.138 3.93e-05 ***
DroughtTrtExt (90)             -2.987      7.649  19.272  -0.390 0.700462    
ageClassPioneer                30.674      7.659  19.413   4.005 0.000731 ***
siteIDTjøtta                    4.638      7.649  19.320   0.606 0.551346    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning in abbreviate(rn, minlength = 11): abbreviate used with non-ASCII chars

Correlation of Fixed Effects:
Warning in abbreviate(rn, minlength = 6): abbreviate used with non-ASCII chars
            (Intr) spcsEn spcsVm spcVv- DTE(90 agClsP
spcsEmptrmn -0.279                                   
spcsVccnmmy -0.284  0.462                            
spcsVccvts- -0.301  0.476  0.456                     
DrghtTE(90) -0.452  0.014  0.027 -0.010              
ageClassPnr -0.474 -0.044 -0.014  0.008 -0.012       
siteIDTjøtt -0.476 -0.017 -0.013 -0.003 -0.013  0.036
# The intercept for LDMC, representing calluna at reference level, is significantly high at 359.3762, indicating a strong baseline effect on LDMC.
# Species Impact: The species Vaccinium vitis-idaea significantly reduces LDMC by 30.0715 compared to the baseline species- unique biological characteristics.
# Drought Treatment: Drought treatment does not significantly affect LDMC, as indicated by a p-value of 0.160270, suggesting drought stress may not be a critical factor for LDMC variation.
# Age Class Influence: Plants classified under the pioneer age class show a significant increase in LDMC (26.5932), pointing towards age or developmental stage as a determinant of LDMC.
# Site Variation: Tjøtta, does not significantly influence LDMC, with a p-value of 0.152627, indicating that location-based environmental factors may not play a significant role in LDMC variation

performance::check_model(model_main_effects_LDMC, detrend = FALSE)

#The Posterior Predictive Check looks reasonable, as the observed data seem to match the model-predicted data well. #The Linearity plot suggests a linear relationship # The Homogeneity of Variance plot does not show an obvious fan shape which would indicate heteroscedasticity, so it seems the assumption of homoscedasticity is met. # The Influential Observations plot indicates a few points with high leverage or large residuals,-but not worrisome as they are extreme values # The Collinearity plot suggests no issues with collinearity since all VIF values are well below the common threshold. # The Normality of the Residuals plot indicates some deviation from normality, especially in the tails. # The Normality of Random Effects plots show some slight deviations from normality #overall, the model fits the data well

fitting model to the ggplot

# Get fitted values directly from the model
fitted_values <- predict(model_main_effects_LDMC, re.form = NA)  # 'NA' to exclude random effects

# Add the fitted values to the filtered_data dataframe
filtered_data$.fitted <- fitted_values

plot <- ggplot(filtered_data, aes(x = species, y = LDMC, fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = .fitted), position = position_dodge(width = 0.75), color = "lightblue", size = 1.5) +
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  labs(title = "LDMC vs Treatment by Species",
       x = "Species", y = "LDMC",
       caption = "Figure 3: Shows overlaid points representing the fitted values of LDMC (Leaf Dry Matter Content) for each species under ambient and extreme drought treatments in two distinct successsional phase and sites.") +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

print(plot)

interaction models

#species * DroughtTrt
model_species_droughtTrt <- lmer(LDMC ~ species * DroughtTrt +
                                    (1 | DroughNet_plotID/plant_nr), 
                                  data = filtered_data)

summary(model_species_droughtTrt)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: LDMC ~ species * DroughtTrt + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 8213.5

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.0489 -0.5788  0.0373  0.5690  5.4632 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept)  258.4   16.07   
 DroughNet_plotID          (Intercept)  407.8   20.20   
 Residual                              2592.5   50.92   
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                                Estimate Std. Error      df
(Intercept)                                      361.849      8.126  41.605
speciesEmpetrum nigrum                            25.164      7.341 725.654
speciesVaccinium myrtillus                        10.122      7.406 694.928
speciesVaccinium vitis-idaea                     -27.718      7.291 691.421
DroughtTrtExt (90)                                 6.215     11.485  41.507
speciesEmpetrum nigrum:DroughtTrtExt (90)        -33.553     10.452 718.944
speciesVaccinium myrtillus:DroughtTrtExt (90)    -18.149     10.914 697.458
speciesVaccinium vitis-idaea:DroughtTrtExt (90)   12.215     10.175 690.821
                                                t value Pr(>|t|)    
(Intercept)                                      44.528  < 2e-16 ***
speciesEmpetrum nigrum                            3.428 0.000642 ***
speciesVaccinium myrtillus                        1.367 0.172144    
speciesVaccinium vitis-idaea                     -3.802 0.000156 ***
DroughtTrtExt (90)                                0.541 0.591342    
speciesEmpetrum nigrum:DroughtTrtExt (90)        -3.210 0.001386 ** 
speciesVaccinium myrtillus:DroughtTrtExt (90)    -1.663 0.096776 .  
speciesVaccinium vitis-idaea:DroughtTrtExt (90)   1.201 0.230325    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) spcsEn spcsVm spcVv- DTE(90 sEn:D( sVm:D(
spcsEmptrmn -0.434                                          
spcsVccnmmy -0.419  0.473                                   
spcsVccvts- -0.427  0.474  0.467                            
DrghtTE(90) -0.708  0.307  0.297  0.302                     
sEn:DTE(90)  0.305 -0.702 -0.332 -0.333 -0.427              
sVm:DTE(90)  0.285 -0.321 -0.679 -0.317 -0.401  0.461       
sVv-:DTE(90  0.306 -0.340 -0.335 -0.717 -0.432  0.475  0.453
# intercept(calluna) LDMC at 365.795 indicate a significant base level of LDMC before considering species variation or drought effects.
# Species-Specific Effects:
# Empetrum nigrum notably increases LDMC by 23.225 units compared to calluna demonstrating- could be a positive adaptation 
# Vaccinium myrtillus also shows a positive but not statistically significant effect on LDMC, suggesting a mild or variable adaptation compared to calluna
# Vaccinium vitis-idaea significantly reduces LDMC by 29.776 units, highlighting its distinct physiological or ecological traits that might contribute to lower LDMC
# Drought Treatment Response:
# drought trt does not significantly alter LDMC on its own
# Interaction with Drought:
# Both Empetrum nigrum and Vaccinium myrtillus exhibit significant negative interactions with drought treatment, indicating a decrease in LDMC under drought condition- suggests these species could be sensitive to drought, affecting their LDMC.
# Vaccinium vitis-idaea shows no significant interaction with drought
#validate model
performance::check_model(model_species_droughtTrt, detrend = FALSE)

Fitting model to plot

# Get fitted values directly from the model
fitted_values <- predict(model_species_droughtTrt, re.form = NA)  # 'NA' to exclude random effects

# Add the fitted values to the filtered_data dataframe
filtered_data$.fitted <- fitted_values

# Now create your plot
plot <- ggplot(filtered_data, aes(x = species, y = LDMC, fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = .fitted), position = position_dodge(width = 0.75), color = "lightblue", size = 1.5) +
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  labs(title = "LDMC vs Treatment by Species",
       x = "Species", y = "LDMC",
       caption = "Figure 3: Shows overlaid points representing the fitted values of LDMC (Leaf Dry Matter Content) for each species under ambient and extreme drought treatments in two distinct successsional phase and sites.") +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

print(plot)

# species * age Class (h2)
#this will help adress the hypothesis by examining weather the effect of drought on trait varies between age classes
#significant interaction supports the hypothesis that mat and pio respond differently to droght conditions, potentially more consrvative traits in mat than pio
LDMC_species_ageClass <- lmer(LDMC ~ species * ageClass +
                                    (1 | DroughNet_plotID/plant_nr), 
                                  data = filtered_data)

summary(LDMC_species_ageClass)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: LDMC ~ species * ageClass + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 8206.3

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.5601 -0.5984  0.0448  0.5778  5.4947 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept)  310.3   17.62   
 DroughNet_plotID          (Intercept)  144.8   12.03   
 Residual                              2593.1   50.92   
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                             Estimate Std. Error      df
(Intercept)                                   348.521      6.714  59.299
speciesEmpetrum nigrum                         24.375      7.707 722.452
speciesVaccinium myrtillus                     -2.709      7.705 708.943
speciesVaccinium vitis-idaea                  -23.650      7.034 686.739
ageClassPioneer                                34.079      9.528  60.118
speciesEmpetrum nigrum:ageClassPioneer        -28.945     10.493 718.463
speciesVaccinium myrtillus:ageClassPioneer     10.354     10.854 699.120
speciesVaccinium vitis-idaea:ageClassPioneer    5.495     10.193 689.002
                                             t value Pr(>|t|)    
(Intercept)                                   51.907  < 2e-16 ***
speciesEmpetrum nigrum                         3.163 0.001629 ** 
speciesVaccinium myrtillus                    -0.352 0.725234    
speciesVaccinium vitis-idaea                  -3.362 0.000817 ***
ageClassPioneer                                3.577 0.000694 ***
speciesEmpetrum nigrum:ageClassPioneer        -2.759 0.005952 ** 
speciesVaccinium myrtillus:ageClassPioneer     0.954 0.340445    
speciesVaccinium vitis-idaea:ageClassPioneer   0.539 0.590026    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) spcsEn spcsVm spcVv- agClsP sEn:CP sVm:CP
spcsEmptrmn -0.489                                          
spcsVccnmmy -0.484  0.456                                   
spcsVccvts- -0.530  0.472  0.471                            
ageClassPnr -0.705  0.344  0.341  0.373                     
spcsEngr:CP  0.359 -0.735 -0.335 -0.347 -0.514              
spcsVmyr:CP  0.343 -0.324 -0.710 -0.334 -0.487  0.461       
spcsVvt-:CP  0.366 -0.326 -0.325 -0.690 -0.521  0.476  0.456
#validate model
performance::check_model(LDMC_species_ageClass, detrend = FALSE)

fitt the fitted values onto the plot

# Get fitted values directly from the model
fitted_values <- predict(LDMC_species_ageClass, re.form = NA)  

filtered_data$.fitted <- fitted_values


plot <- ggplot(filtered_data, aes(x = species, y = LDMC, fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = .fitted), position = position_dodge(width = 0.75), color = "lightblue", size = 1.5) +
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  labs(title = "LDMC vs Treatment by Species",
       x = "Species", y = "LDMC",
       caption = "Figure 3: Shows overlaid points representing the fitted values of LDMC (Leaf Dry Matter Content) for each species under ambient and extreme drought treatments in two distinct successsional phase and sites.") +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

print(plot)

# Drought Treatment * siteID (related to h3)
#will help to show impact between north and south
# significant interaction would indicate regional variability in how drought influences trait- hence supportinng the hypothesis, otherwise then..
model1_species_siteID <- lmer(LDMC ~ species * siteID + 
                                  (1 | DroughNet_plotID/plant_nr), 
                                data = filtered_data)
summary(model1_species_siteID)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: LDMC ~ species * siteID + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 8150.9

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.6641 -0.5989  0.0624  0.5847  6.2545 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept)  361.0   19.00   
 DroughNet_plotID          (Intercept)  326.1   18.06   
 Residual                              2347.7   48.45   
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                          Estimate Std. Error      df t value
(Intercept)                                369.128      7.766  43.839  47.529
speciesEmpetrum nigrum                      25.754      7.581 746.502   3.397
speciesVaccinium myrtillus                   4.138      7.650 693.341   0.541
speciesVaccinium vitis-idaea               -56.769      7.087 687.616  -8.011
siteIDTjøtta                                -7.349     10.908  42.636  -0.674
speciesEmpetrum nigrum:siteIDTjøtta        -26.068     10.087 725.243  -2.584
speciesVaccinium myrtillus:siteIDTjøtta     -1.468     10.402 691.426  -0.141
speciesVaccinium vitis-idaea:siteIDTjøtta   64.993      9.721 685.887   6.686
                                          Pr(>|t|)    
(Intercept)                                < 2e-16 ***
speciesEmpetrum nigrum                    0.000717 ***
speciesVaccinium myrtillus                0.588777    
speciesVaccinium vitis-idaea              4.89e-15 ***
siteIDTjøtta                              0.504115    
speciesEmpetrum nigrum:siteIDTjøtta       0.009952 ** 
speciesVaccinium myrtillus:siteIDTjøtta   0.887791    
speciesVaccinium vitis-idaea:siteIDTjøtta 4.77e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning in abbreviate(rn, minlength = 11): abbreviate used with non-ASCII chars

Correlation of Fixed Effects:
Warning in abbreviate(rn, minlength = 6): abbreviate used with non-ASCII chars
            (Intr) spcsEn spcsVm spcVv- stIDTj sEn:ID sVm:ID
spcsEmptrmn -0.426                                          
spcsVccnmmy -0.400  0.443                                   
spcsVccvts- -0.434  0.431  0.426                            
siteIDTjøtt -0.712  0.303  0.285  0.309                     
spcsEng:IDT  0.320 -0.752 -0.333 -0.324 -0.429              
spcsVmy:IDT  0.295 -0.326 -0.735 -0.313 -0.403  0.459       
spcsVv-:IDT  0.316 -0.314 -0.311 -0.729 -0.433  0.466  0.450
#validate model
performance::check_model(model1_species_siteID, detrend = FALSE)

# Get fitted values directly from the model
fitted_values <- predict(model1_species_siteID, re.form = NA)  # 'NA' to exclude random effects

# Add the fitted values to the filtered_data dataframe
filtered_data$fitted <- fitted_values  

plot <- ggplot(filtered_data, aes(x = species, y = LDMC, fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = fitted), position = position_dodge(width = 0.75), color = "brown", size = 1.5) +
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(
    axis.text.x = element_text(angle = 90, hjust = 1),
    plot.margin = unit(c(1, 1, 2, 1), "lines"),  
    plot.caption = element_text(hjust = 0.5)  
  ) +
  labs(
    title = "LDMC vs Treatment by Species",
    x = "Species", y = "LDMC",
    caption = "Figure 1: Shows LDMC of the four species under ambient and extreme drought conditions in two distinct successional phases (pioneer nad Mature) and two distinct sites (Tjøtta in the north and Lygra in the south)."
  ) +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

print(plot)

model_interactions <- lmer(LDMC ~ (species + DroughtTrt + ageClass +  siteID)^3 +
                                        (1 | DroughNet_plotID/plant_nr),
                           data = filtered_data)
summary(model_interactions)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: 
LDMC ~ (species + DroughtTrt + ageClass + siteID)^3 + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 7920.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.7934 -0.5330  0.0410  0.5691  6.1409 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept)  286.7   16.93   
 DroughNet_plotID          (Intercept)  111.3   10.55   
 Residual                              2211.7   47.03   
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                                                Estimate
(Intercept)                                                      348.442
speciesEmpetrum nigrum                                            58.353
speciesVaccinium myrtillus                                        -5.864
speciesVaccinium vitis-idaea                                     -75.218
DroughtTrtExt (90)                                                12.022
ageClassPioneer                                                   17.227
siteIDTjøtta                                                      16.022
speciesEmpetrum nigrum:DroughtTrtExt (90)                        -35.815
speciesVaccinium myrtillus:DroughtTrtExt (90)                    -18.923
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   19.667
speciesEmpetrum nigrum:ageClassPioneer                            -2.143
speciesVaccinium myrtillus:ageClassPioneer                        47.789
speciesVaccinium vitis-idaea:ageClassPioneer                      29.627
speciesEmpetrum nigrum:siteIDTjøtta                              -43.735
speciesVaccinium myrtillus:siteIDTjøtta                            2.639
speciesVaccinium vitis-idaea:siteIDTjøtta                         77.652
DroughtTrtExt (90):ageClassPioneer                                19.944
DroughtTrtExt (90):siteIDTjøtta                                  -56.036
ageClassPioneer:siteIDTjøtta                                     -14.722
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer        -43.891
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer    -41.649
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer  -21.419
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta            50.144
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta        41.437
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      12.115
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta              -20.368
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta          -32.718
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta        -39.383
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                   53.576
                                                                Std. Error
(Intercept)                                                         12.090
speciesEmpetrum nigrum                                              14.245
speciesVaccinium myrtillus                                          13.280
speciesVaccinium vitis-idaea                                        12.184
DroughtTrtExt (90)                                                  16.746
ageClassPioneer                                                     16.711
siteIDTjøtta                                                        16.549
speciesEmpetrum nigrum:DroughtTrtExt (90)                           18.772
speciesVaccinium myrtillus:DroughtTrtExt (90)                       20.329
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                     16.104
speciesEmpetrum nigrum:ageClassPioneer                              17.626
speciesVaccinium myrtillus:ageClassPioneer                          17.302
speciesVaccinium vitis-idaea:ageClassPioneer                        17.300
speciesEmpetrum nigrum:siteIDTjøtta                                 17.388
speciesVaccinium myrtillus:siteIDTjøtta                             17.061
speciesVaccinium vitis-idaea:siteIDTjøtta                           16.064
DroughtTrtExt (90):ageClassPioneer                                  22.219
DroughtTrtExt (90):siteIDTjøtta                                     22.144
ageClassPioneer:siteIDTjøtta                                        22.183
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer           19.565
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer       20.954
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer     18.962
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta              19.675
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta          21.106
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta        18.971
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta                 19.832
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta             20.910
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta           19.008
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                     27.237
                                                                     df t value
(Intercept)                                                      37.610  28.820
speciesEmpetrum nigrum                                          709.801   4.096
speciesVaccinium myrtillus                                      662.963  -0.442
speciesVaccinium vitis-idaea                                    653.414  -6.173
DroughtTrtExt (90)                                               34.607   0.718
ageClassPioneer                                                  34.274   1.031
siteIDTjøtta                                                     32.969   0.968
speciesEmpetrum nigrum:DroughtTrtExt (90)                       708.023  -1.908
speciesVaccinium myrtillus:DroughtTrtExt (90)                   685.693  -0.931
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 656.831   1.221
speciesEmpetrum nigrum:ageClassPioneer                          726.011  -0.122
speciesVaccinium myrtillus:ageClassPioneer                      679.171   2.762
speciesVaccinium vitis-idaea:ageClassPioneer                    684.756   1.713
speciesEmpetrum nigrum:siteIDTjøtta                             711.770  -2.515
speciesVaccinium myrtillus:siteIDTjøtta                         677.512   0.155
speciesVaccinium vitis-idaea:siteIDTjøtta                       672.952   4.834
DroughtTrtExt (90):ageClassPioneer                               26.765   0.898
DroughtTrtExt (90):siteIDTjøtta                                  26.424  -2.530
ageClassPioneer:siteIDTjøtta                                     26.575  -0.664
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer       697.833  -2.243
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer   682.842  -1.988
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 676.999  -1.130
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta          709.469   2.549
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta      684.063   1.963
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    676.524   0.639
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta             709.569  -1.027
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta         683.239  -1.565
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       678.870  -2.072
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  15.046   1.967
                                                                Pr(>|t|)    
(Intercept)                                                      < 2e-16 ***
speciesEmpetrum nigrum                                          4.68e-05 ***
speciesVaccinium myrtillus                                        0.6589    
speciesVaccinium vitis-idaea                                    1.17e-09 ***
DroughtTrtExt (90)                                                0.4776    
ageClassPioneer                                                   0.3098    
siteIDTjøtta                                                      0.3400    
speciesEmpetrum nigrum:DroughtTrtExt (90)                         0.0568 .  
speciesVaccinium myrtillus:DroughtTrtExt (90)                     0.3522    
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.2224    
speciesEmpetrum nigrum:ageClassPioneer                            0.9033    
speciesVaccinium myrtillus:ageClassPioneer                        0.0059 ** 
speciesVaccinium vitis-idaea:ageClassPioneer                      0.0873 .  
speciesEmpetrum nigrum:siteIDTjøtta                               0.0121 *  
speciesVaccinium myrtillus:siteIDTjøtta                           0.8771    
speciesVaccinium vitis-idaea:siteIDTjøtta                       1.66e-06 ***
DroughtTrtExt (90):ageClassPioneer                                0.3774    
DroughtTrtExt (90):siteIDTjøtta                                   0.0177 *  
ageClassPioneer:siteIDTjøtta                                      0.5126    
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer         0.0252 *  
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer     0.0473 *  
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   0.2591    
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta            0.0110 *  
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta        0.0500 .  
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.5233    
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta               0.3048    
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta           0.1181    
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.0386 *  
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                   0.0679 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation matrix not shown by default, as p = 29 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
#validate model
performance::check_model(model_interactions, detrend = FALSE)

Trait 2- plant height

#model with all the main effects
model_main_effects <- lmer(plant_height ~ species + DroughtTrt + ageClass + siteID +
                           (1 | DroughNet_plotID/plant_nr),
                           data = filtered_data)


summary(model_main_effects)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: plant_height ~ species + DroughtTrt + ageClass + siteID + (1 |  
    DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 4558.6

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.7321 -0.5753 -0.0484  0.6013  4.0400 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept)  3.410   1.847   
 DroughNet_plotID          (Intercept)  6.381   2.526   
 Residual                              19.915   4.463   
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                             Estimate Std. Error       df t value Pr(>|t|)    
(Intercept)                   26.2221     1.1926  22.1651  21.987  < 2e-16 ***
speciesEmpetrum nigrum        -5.5906     0.4611 716.9459 -12.123  < 2e-16 ***
speciesVaccinium myrtillus    -9.6354     0.4782 696.0138 -20.150  < 2e-16 ***
speciesVaccinium vitis-idaea -10.8049     0.4470 693.9222 -24.174  < 2e-16 ***
DroughtTrtExt (90)             3.3234     1.1615  19.9300   2.861 0.009673 ** 
ageClassPioneer               -4.3616     1.1619  19.9685  -3.754 0.001253 ** 
siteIDTjøtta                  -5.1761     1.1614  19.9289  -4.457 0.000244 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning in abbreviate(rn, minlength = 11): abbreviate used with non-ASCII chars

Correlation of Fixed Effects:
Warning in abbreviate(rn, minlength = 6): abbreviate used with non-ASCII chars
            (Intr) spcsEn spcsVm spcVv- DTE(90 agClsP
spcsEmptrmn -0.167                                   
spcsVccnmmy -0.170  0.463                            
spcsVccvts- -0.181  0.473  0.454                     
DrghtTE(90) -0.482  0.009  0.017 -0.006              
ageClassPnr -0.492 -0.028 -0.009  0.004 -0.004       
siteIDTjøtt -0.492 -0.010 -0.008 -0.001 -0.005  0.015
performance::check_model(model_main_effects, detrend = FALSE)

#the model does not show any normality of residuals and also there is heterogeneity of variance
#need to modify by transforming the fitted values


#plant heightneeds to be log transformed to achieve homoscedasticity and linearity
model_main_effects3 <- lmer(log(plant_height) ~ species + DroughtTrt + ageClass + siteID +
                           (1 | DroughNet_plotID/plant_nr),
                           data = filtered_data)


summary(model_main_effects3)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(plant_height) ~ species + DroughtTrt + ageClass + siteID +  
    (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 188.8

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.97832 -0.62162  0.01327  0.64119  2.77955 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.01764  0.1328  
 DroughNet_plotID          (Intercept) 0.03083  0.1756  
 Residual                              0.06010  0.2452  
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                              Estimate Std. Error        df t value Pr(>|t|)
(Intercept)                    3.24672    0.08126  21.26656  39.956  < 2e-16
speciesEmpetrum nigrum        -0.27831    0.02548 713.70008 -10.921  < 2e-16
speciesVaccinium myrtillus    -0.53579    0.02635 696.22629 -20.331  < 2e-16
speciesVaccinium vitis-idaea  -0.60639    0.02463 695.59109 -24.624  < 2e-16
DroughtTrtExt (90)             0.19009    0.07985  19.82276   2.381  0.02744
ageClassPioneer               -0.26757    0.07987  19.85403  -3.350  0.00321
siteIDTjøtta                  -0.28991    0.07985  19.82382  -3.631  0.00168
                                
(Intercept)                  ***
speciesEmpetrum nigrum       ***
speciesVaccinium myrtillus   ***
speciesVaccinium vitis-idaea ***
DroughtTrtExt (90)           *  
ageClassPioneer              ** 
siteIDTjøtta                 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning in abbreviate(rn, minlength = 11): abbreviate used with non-ASCII chars

Correlation of Fixed Effects:
Warning in abbreviate(rn, minlength = 6): abbreviate used with non-ASCII chars
            (Intr) spcsEn spcsVm spcVv- DTE(90 agClsP
spcsEmptrmn -0.135                                   
spcsVccnmmy -0.137  0.463                            
spcsVccvts- -0.146  0.473  0.454                     
DrghtTE(90) -0.487  0.008  0.014 -0.005              
ageClassPnr -0.497 -0.024 -0.008  0.002 -0.003       
siteIDTjøtt -0.495 -0.007 -0.006  0.001 -0.004  0.014
# Species: Empetrum nigrum, Vaccinium myrtillus, and Vaccinium vitis-idaea all show significant decreases in height compared to Calluna, indicating notable species-specific differences.
# Drought Treatment: drought positively affects height, suggesting an increase under drought conditions for all species
# Age Class: The pioneer age class is associated with a significant decrease in height, indicating lower levels compared to more mature.
# Site: The Tjøtta site is linked to a decrease in height, highlighting the influence of location on height
#validate the model- check for linearity, homoscedasticity, outliers by plotting the resuduals

performance::check_model(model_main_effects3, detrend = FALSE)

fitt model to plot

# Get fitted values directly from the model
fitted_values <- predict(model_main_effects3, re.form = NA)  # 'NA' to exclude random effects

# Exponentiate the fitted values to transform back to the original scale
filtered_data$fitted <- exp(fitted_values)


plot <- ggplot(filtered_data, aes(x = species, y = plant_height, fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = fitted), position = position_dodge(width = 0.75), color = "brown", size = 1.5) +  
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(
    axis.text.x = element_text(angle = 90, hjust = 1),
    plot.margin = unit(c(1, 1, 2, 1), "lines"),  
    plot.caption = element_text(hjust = 0.5)  
  ) +
  labs(
    title = "Plant Height vs Treatment by Species",
    x = "Species", y = "Plant Height",  # Updated y-axis label
    caption = "Figure 1: Shows plant height of the four species under ambient and extreme drought conditions in two distinct successional phases (pioneer and mature) and two distinct sites (Tjøtta in the north and Lygra in the south)."
  ) +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

# Print the plot
print(plot)

interaction models

#models for two way interactions
#species * drought trt
model_species_drought2 <- lmer(log(plant_height) ~ species * DroughtTrt +
                              (1 | DroughNet_plotID/plant_nr),
                              data = filtered_data)
summary(model_species_drought2)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: 
log(plant_height) ~ species * DroughtTrt + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 185.6

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-3.15184 -0.61876  0.00894  0.60779  2.71992 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.01890  0.1375  
 DroughNet_plotID          (Intercept) 0.06913  0.2629  
 Residual                              0.05782  0.2405  
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                                 Estimate Std. Error        df
(Intercept)                                       3.01878    0.08256  24.71359
speciesEmpetrum nigrum                           -0.29503    0.03523 712.90507
speciesVaccinium myrtillus                       -0.63494    0.03522 690.91870
speciesVaccinium vitis-idaea                     -0.70578    0.03465 688.84107
DroughtTrtExt (90)                                0.08853    0.11675  24.70277
speciesEmpetrum nigrum:DroughtTrtExt (90)         0.03177    0.05007 707.79820
speciesVaccinium myrtillus:DroughtTrtExt (90)     0.21019    0.05198 690.36941
speciesVaccinium vitis-idaea:DroughtTrtExt (90)   0.19295    0.04836 690.65596
                                                t value Pr(>|t|)    
(Intercept)                                      36.564  < 2e-16 ***
speciesEmpetrum nigrum                           -8.374 2.94e-16 ***
speciesVaccinium myrtillus                      -18.025  < 2e-16 ***
speciesVaccinium vitis-idaea                    -20.369  < 2e-16 ***
DroughtTrtExt (90)                                0.758    0.455    
speciesEmpetrum nigrum:DroughtTrtExt (90)         0.635    0.526    
speciesVaccinium myrtillus:DroughtTrtExt (90)     4.044 5.85e-05 ***
speciesVaccinium vitis-idaea:DroughtTrtExt (90)   3.990 7.32e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) spcsEn spcsVm spcVv- DTE(90 sEn:D( sVm:D(
spcsEmptrmn -0.205                                          
spcsVccnmmy -0.195  0.472                                   
spcsVccvts- -0.199  0.473  0.469                            
DrghtTE(90) -0.707  0.145  0.138  0.141                     
sEn:DTE(90)  0.144 -0.704 -0.332 -0.333 -0.200              
sVm:DTE(90)  0.132 -0.320 -0.678 -0.318 -0.186  0.462       
sVv-:DTE(90  0.143 -0.339 -0.336 -0.716 -0.202  0.473  0.453
# Compared to Calluna, the other species significantly reduce the height, with Vaccinium species showing the largest decreases.
# Drought treatment on its own does not significantly affect theight, but its interaction with species (Vaccinium myrtillus and Vaccinium vitis-idaea) leads to significant increases, suggesting these species may respond positively to drought conditions in terms of thier height

#plot diagnostic plots
performance::check_model(model_species_drought2, detrend = FALSE)

# Get fitted values directly from the model
fitted_values <- predict(model_species_drought2, re.form = NA)  

# Add the fitted values to the filtered_data dataframe
filtered_data$.fitted <- fitted_values

plot <- ggplot(filtered_data, aes(x = species, y = log(plant_height), fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = .fitted), position = position_dodge(width = 0.75), color = "red", size = 1.5) +
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  labs(title = "plant height vs Treatment by Species",
       x = "Species", y = "LDMC") +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

print(plot)

#species *age class
model_height_species_ageclass <- lmer(log(plant_height) ~ species * ageClass +
                          (1 | DroughNet_plotID/plant_nr),
                          data = filtered_data)
                          
                  

summary(model_height_species_ageclass)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: 
log(plant_height) ~ species * ageClass + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 190.8

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.7335 -0.6384  0.0066  0.5947  2.8680 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.01762  0.1327  
 DroughNet_plotID          (Intercept) 0.06058  0.2461  
 Residual                              0.05872  0.2423  
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                               Estimate Std. Error         df
(Intercept)                                    3.212515   0.077934  25.253042
speciesEmpetrum nigrum                        -0.250618   0.037282 708.693041
speciesVaccinium myrtillus                    -0.537803   0.037102 699.298345
speciesVaccinium vitis-idaea                  -0.680448   0.033656 694.285819
ageClassPioneer                               -0.298103   0.110259  25.292530
speciesEmpetrum nigrum:ageClassPioneer        -0.045231   0.050633 708.563863
speciesVaccinium myrtillus:ageClassPioneer     0.003914   0.052144 692.362294
speciesVaccinium vitis-idaea:ageClassPioneer   0.160995   0.048800 692.879297
                                             t value Pr(>|t|)    
(Intercept)                                   41.221  < 2e-16 ***
speciesEmpetrum nigrum                        -6.722 3.68e-11 ***
speciesVaccinium myrtillus                   -14.495  < 2e-16 ***
speciesVaccinium vitis-idaea                 -20.218  < 2e-16 ***
ageClassPioneer                               -2.704  0.01209 *  
speciesEmpetrum nigrum:ageClassPioneer        -0.893  0.37199    
speciesVaccinium myrtillus:ageClassPioneer     0.075  0.94019    
speciesVaccinium vitis-idaea:ageClassPioneer   3.299  0.00102 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) spcsEn spcsVm spcVv- agClsP sEn:CP sVm:CP
spcsEmptrmn -0.199                                          
spcsVccnmmy -0.197  0.466                                   
spcsVccvts- -0.218  0.472  0.473                            
ageClassPnr -0.707  0.141  0.139  0.154                     
spcsEngr:CP  0.147 -0.736 -0.343 -0.348 -0.212              
spcsVmyr:CP  0.140 -0.332 -0.712 -0.336 -0.199  0.463       
spcsVvt-:CP  0.150 -0.326 -0.326 -0.690 -0.215  0.472  0.453
#plot diagnostic plots
performance::check_model(model_height_species_ageclass, detrend = FALSE)

# Get fitted values directly from the model
fitted_values <- predict(model_height_species_ageclass, re.form = NA) 

# Add the fitted values to the filtered_data dataframe
filtered_data$.fitted <- fitted_values

# Now create your plot
plot <- ggplot(filtered_data, aes(x = species, y = log(plant_height), fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = .fitted), position = position_dodge(width = 0.75), color = "red", size = 1.5) +
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  labs(title = "plant height vs Treatment by Species",
       x = "Species", y = "plant height") +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

print(plot)

#drought * siteID
model_species_siteID <- lmer(log(plant_height) ~ species * siteID +
                           (1 | DroughNet_plotID/plant_nr),
                           data = filtered_data)
summary(model_species_siteID)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(plant_height) ~ species * siteID + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 155.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.8155 -0.6371  0.0412  0.6668  2.7554 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.01791  0.1338  
 DroughNet_plotID          (Intercept) 0.05680  0.2383  
 Residual                              0.05583  0.2363  
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                           Estimate Std. Error        df
(Intercept)                                 3.31067    0.07588  25.44377
speciesEmpetrum nigrum                     -0.39822    0.03774 730.58385
speciesVaccinium myrtillus                 -0.67939    0.03759 689.56952
speciesVaccinium vitis-idaea               -0.78182    0.03473 691.16901
siteIDTjøtta                               -0.48665    0.10718  25.32183
speciesEmpetrum nigrum:siteIDTjøtta         0.22678    0.04986 716.66403
speciesVaccinium myrtillus:siteIDTjøtta     0.27250    0.05106 691.03506
speciesVaccinium vitis-idaea:siteIDTjøtta   0.33325    0.04763 691.61858
                                          t value Pr(>|t|)    
(Intercept)                                43.631  < 2e-16 ***
speciesEmpetrum nigrum                    -10.553  < 2e-16 ***
speciesVaccinium myrtillus                -18.075  < 2e-16 ***
speciesVaccinium vitis-idaea              -22.511  < 2e-16 ***
siteIDTjøtta                               -4.540 0.000119 ***
speciesEmpetrum nigrum:siteIDTjøtta         4.548 6.35e-06 ***
speciesVaccinium myrtillus:siteIDTjøtta     5.337 1.28e-07 ***
speciesVaccinium vitis-idaea:siteIDTjøtta   6.997 6.17e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning in abbreviate(rn, minlength = 11): abbreviate used with non-ASCII chars

Correlation of Fixed Effects:
Warning in abbreviate(rn, minlength = 6): abbreviate used with non-ASCII chars
            (Intr) spcsEn spcsVm spcVv- stIDTj sEn:ID sVm:ID
spcsEmptrmn -0.213                                          
spcsVccnmmy -0.199  0.441                                   
spcsVccvts- -0.217  0.419  0.419                            
siteIDTjøtt -0.708  0.151  0.141  0.154                     
spcsEng:IDT  0.162 -0.757 -0.334 -0.317 -0.213              
spcsVmy:IDT  0.146 -0.325 -0.736 -0.308 -0.199  0.459       
spcsVv-:IDT  0.158 -0.305 -0.306 -0.729 -0.216  0.461  0.448
#plot diagnostic plots
performance::check_model(model_species_siteID, detrend = FALSE)

model_three_interactions <- lmer(log(plant_height) ~ (species + DroughtTrt + ageClass +  siteID)^3 +
                                        (1 | DroughNet_plotID/plant_nr),
                           data = filtered_data)
summary(model_three_interactions)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(plant_height) ~ (species + DroughtTrt + ageClass + siteID)^3 +  
    (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 137.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.7057 -0.6124  0.0235  0.5838  2.6755 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.02021  0.1422  
 DroughNet_plotID          (Intercept) 0.02858  0.1691  
 Residual                              0.05152  0.2270  
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                                                  Estimate
(Intercept)                                                       3.327523
speciesEmpetrum nigrum                                           -0.401696
speciesVaccinium myrtillus                                       -0.730645
speciesVaccinium vitis-idaea                                     -0.904984
DroughtTrtExt (90)                                                0.150106
ageClassPioneer                                                  -0.146888
siteIDTjøtta                                                     -0.453777
speciesEmpetrum nigrum:DroughtTrtExt (90)                         0.102568
speciesVaccinium myrtillus:DroughtTrtExt (90)                     0.216975
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.141450
speciesEmpetrum nigrum:ageClassPioneer                           -0.062976
speciesVaccinium myrtillus:ageClassPioneer                       -0.152946
speciesVaccinium vitis-idaea:ageClassPioneer                     -0.046222
speciesEmpetrum nigrum:siteIDTjøtta                               0.264710
speciesVaccinium myrtillus:siteIDTjøtta                           0.287906
speciesVaccinium vitis-idaea:siteIDTjøtta                         0.390425
DroughtTrtExt (90):ageClassPioneer                               -0.078432
DroughtTrtExt (90):siteIDTjøtta                                   0.148020
ageClassPioneer:siteIDTjøtta                                     -0.020588
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer         0.006639
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer     0.197433
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   0.289825
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta           -0.126789
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta       -0.191167
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta     -0.160334
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta               0.014920
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta           0.099074
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.052126
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -0.389352
                                                                Std. Error
(Intercept)                                                       0.116129
speciesEmpetrum nigrum                                            0.070821
speciesVaccinium myrtillus                                        0.064360
speciesVaccinium vitis-idaea                                      0.058940
DroughtTrtExt (90)                                                0.163669
ageClassPioneer                                                   0.162773
siteIDTjøtta                                                      0.162820
speciesEmpetrum nigrum:DroughtTrtExt (90)                         0.092712
speciesVaccinium myrtillus:DroughtTrtExt (90)                     0.099642
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.077962
speciesEmpetrum nigrum:ageClassPioneer                            0.087379
speciesVaccinium myrtillus:ageClassPioneer                        0.084150
speciesVaccinium vitis-idaea:ageClassPioneer                      0.084242
speciesEmpetrum nigrum:siteIDTjøtta                               0.085777
speciesVaccinium myrtillus:siteIDTjøtta                           0.082981
speciesVaccinium vitis-idaea:siteIDTjøtta                         0.078034
DroughtTrtExt (90):ageClassPioneer                                0.227082
DroughtTrtExt (90):siteIDTjøtta                                   0.227407
ageClassPioneer:siteIDTjøtta                                      0.227316
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer         0.095786
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer     0.102276
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   0.092200
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta            0.096720
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta        0.103056
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.092228
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta               0.097556
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta           0.102016
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.092463
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                   0.312610
                                                                        df
(Intercept)                                                      19.662710
speciesEmpetrum nigrum                                          707.510008
speciesVaccinium myrtillus                                      664.052688
speciesVaccinium vitis-idaea                                    661.135537
DroughtTrtExt (90)                                               19.398579
ageClassPioneer                                                  18.963335
siteIDTjøtta                                                     18.989844
speciesEmpetrum nigrum:DroughtTrtExt (90)                       695.643768
speciesVaccinium myrtillus:DroughtTrtExt (90)                   673.269314
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 663.505052
speciesEmpetrum nigrum:ageClassPioneer                          709.542998
speciesVaccinium myrtillus:ageClassPioneer                      672.646802
speciesVaccinium vitis-idaea:ageClassPioneer                    675.950151
speciesEmpetrum nigrum:siteIDTjøtta                             699.876488
speciesVaccinium myrtillus:siteIDTjøtta                         674.242722
speciesVaccinium vitis-idaea:siteIDTjøtta                       674.616442
DroughtTrtExt (90):ageClassPioneer                               17.958921
DroughtTrtExt (90):siteIDTjøtta                                  18.064266
ageClassPioneer:siteIDTjøtta                                     18.036959
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer       687.126669
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer   673.421613
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 675.830691
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta          695.962213
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta      672.981793
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    675.533497
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta             695.732872
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta         673.358060
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       677.023668
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  16.126652
                                                                t value
(Intercept)                                                      28.654
speciesEmpetrum nigrum                                           -5.672
speciesVaccinium myrtillus                                      -11.353
speciesVaccinium vitis-idaea                                    -15.354
DroughtTrtExt (90)                                                0.917
ageClassPioneer                                                  -0.902
siteIDTjøtta                                                     -2.787
speciesEmpetrum nigrum:DroughtTrtExt (90)                         1.106
speciesVaccinium myrtillus:DroughtTrtExt (90)                     2.178
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   1.814
speciesEmpetrum nigrum:ageClassPioneer                           -0.721
speciesVaccinium myrtillus:ageClassPioneer                       -1.818
speciesVaccinium vitis-idaea:ageClassPioneer                     -0.549
speciesEmpetrum nigrum:siteIDTjøtta                               3.086
speciesVaccinium myrtillus:siteIDTjøtta                           3.470
speciesVaccinium vitis-idaea:siteIDTjøtta                         5.003
DroughtTrtExt (90):ageClassPioneer                               -0.345
DroughtTrtExt (90):siteIDTjøtta                                   0.651
ageClassPioneer:siteIDTjøtta                                     -0.091
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer         0.069
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer     1.930
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   3.143
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta           -1.311
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta       -1.855
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta     -1.738
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta               0.153
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta           0.971
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.564
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -1.245
                                                                Pr(>|t|)    
(Intercept)                                                      < 2e-16 ***
speciesEmpetrum nigrum                                          2.06e-08 ***
speciesVaccinium myrtillus                                       < 2e-16 ***
speciesVaccinium vitis-idaea                                     < 2e-16 ***
DroughtTrtExt (90)                                              0.370335    
ageClassPioneer                                                 0.378158    
siteIDTjøtta                                                    0.011756 *  
speciesEmpetrum nigrum:DroughtTrtExt (90)                       0.268973    
speciesVaccinium myrtillus:DroughtTrtExt (90)                   0.029786 *  
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 0.070076 .  
speciesEmpetrum nigrum:ageClassPioneer                          0.471315    
speciesVaccinium myrtillus:ageClassPioneer                      0.069579 .  
speciesVaccinium vitis-idaea:ageClassPioneer                    0.583402    
speciesEmpetrum nigrum:siteIDTjøtta                             0.002109 ** 
speciesVaccinium myrtillus:siteIDTjøtta                         0.000555 ***
speciesVaccinium vitis-idaea:siteIDTjøtta                       7.20e-07 ***
DroughtTrtExt (90):ageClassPioneer                              0.733813    
DroughtTrtExt (90):siteIDTjøtta                                 0.523302    
ageClassPioneer:siteIDTjøtta                                    0.928831    
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer       0.944758    
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer   0.053979 .  
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 0.001743 ** 
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta          0.190329    
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta      0.064036 .  
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    0.082586 .  
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta             0.878490    
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta         0.331817    
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       0.573110    
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                 0.230746    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation matrix not shown by default, as p = 29 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
#validate model
performance::check_model(model_three_interactions, detrend = FALSE)

Trait 3- SLA

# model for sla with all the fixed effects
model_main_effects <- lmer(SLA ~ species + DroughtTrt + ageClass + siteID +
                           (1 | DroughNet_plotID/plant_nr),
                           data = filtered_data)

summary(model_main_effects)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: 
SLA ~ species + DroughtTrt + ageClass + siteID + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: 7482.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.5193 -0.5305 -0.0876  0.3306  6.3637 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 104.28   10.212  
 DroughNet_plotID          (Intercept)  39.66    6.298  
 Residual                              996.03   31.560  
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                             Estimate Std. Error      df t value Pr(>|t|)    
(Intercept)                    87.651      4.588  29.915  19.105  < 2e-16 ***
speciesEmpetrum nigrum         42.415      3.233 730.780  13.121  < 2e-16 ***
speciesVaccinium myrtillus    155.145      3.359 715.032  46.183  < 2e-16 ***
speciesVaccinium vitis-idaea   45.801      3.151 706.068  14.537  < 2e-16 ***
DroughtTrtExt (90)             -3.031      4.171  20.348  -0.727 0.475771    
ageClassPioneer               -10.719      4.179  20.569  -2.565 0.018221 *  
siteIDTjøtta                  -16.294      4.172  20.439  -3.905 0.000849 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning in abbreviate(rn, minlength = 11): abbreviate used with non-ASCII chars

Correlation of Fixed Effects:
Warning in abbreviate(rn, minlength = 6): abbreviate used with non-ASCII chars
            (Intr) spcsEn spcsVm spcVv- DTE(90 agClsP
spcsEmptrmn -0.309                                   
spcsVccnmmy -0.314  0.462                            
spcsVccvts- -0.333  0.477  0.457                     
DrghtTE(90) -0.441  0.015  0.029 -0.012              
ageClassPnr -0.467 -0.048 -0.015  0.009 -0.014       
siteIDTjøtt -0.470 -0.018 -0.014 -0.003 -0.015  0.044
performance::check_model(model_main_effects, detrend = FALSE)

##the model does not fit the data well
#need to transform the observed values to achive normality and homoogeneity of variance


#log transform SLA to achive normality and homodeneity of variances
model_main_effects4 <- lmer(log(SLA) ~ species + DroughtTrt + ageClass + siteID +
                           (1 | DroughNet_plotID/plant_nr),
                           data = filtered_data)

summary(model_main_effects4)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: 
log(SLA) ~ species + DroughtTrt + ageClass + siteID + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: -133.8

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.2558 -0.5792 -0.0635  0.5222  3.2135 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.005324 0.07297 
 DroughNet_plotID          (Intercept) 0.001795 0.04236 
 Residual                              0.042768 0.20680 
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                               Estimate Std. Error         df t value Pr(>|t|)
(Intercept)                    4.373178   0.031036  28.010849 140.907  < 2e-16
speciesEmpetrum nigrum         0.457574   0.021221 723.224265  21.563  < 2e-16
speciesVaccinium myrtillus     1.134496   0.022039 703.719975  51.476  < 2e-16
speciesVaccinium vitis-idaea   0.455653   0.020664 694.265373  22.050  < 2e-16
DroughtTrtExt (90)            -0.003061   0.028388  19.502029  -0.108 0.915241
ageClassPioneer               -0.081935   0.028439  19.716246  -2.881 0.009325
siteIDTjøtta                  -0.119785   0.028394  19.589008  -4.219 0.000439
                                
(Intercept)                  ***
speciesEmpetrum nigrum       ***
speciesVaccinium myrtillus   ***
speciesVaccinium vitis-idaea ***
DroughtTrtExt (90)              
ageClassPioneer              ** 
siteIDTjøtta                 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning in abbreviate(rn, minlength = 11): abbreviate used with non-ASCII chars

Correlation of Fixed Effects:
Warning in abbreviate(rn, minlength = 6): abbreviate used with non-ASCII chars
            (Intr) spcsEn spcsVm spcVv- DTE(90 agClsP
spcsEmptrmn -0.300                                   
spcsVccnmmy -0.304  0.462                            
spcsVccvts- -0.322  0.477  0.457                     
DrghtTE(90) -0.444  0.015  0.029 -0.011              
ageClassPnr -0.470 -0.048 -0.015  0.008 -0.014       
siteIDTjøtt -0.472 -0.017 -0.013 -0.003 -0.015  0.044
# Calluna exhibits a significant baseline SLA value of 4.327885, serving as the reference for other species comparisons.
# Species Effects:
# Empetrum nigrum Significantly increases SLA by 0.519248 compared to Calluna.
# Vaccinium myrtillus Shows a substantial increase in SLA by 1.195279, the largest among the species.
# Vaccinium vitis-idaea also significantly increases SLA by 0.513608, similar to Empetrum nigrum.
# All species effects are highly significant, indicating distinct SLA characteristics compared to Calluna.
# Drought treatment effect on SLA is negligible (-0.001773) and not statistically significant, suggesting drought has minimal/no impact on SLA across the specie
# Age Class (Pioneer)indicates a significant decrease in SLA (-0.083333), suggesting pioneer plants have a lower SLA compared to more mature stages.
# Site (Tjøtta): Associated with a significant decrease in SLA (-0.152224), indicating environmental or locational factors at Tjøtta contribute to lower SLA values

#validate the model- check for linearity, homoscedasticity, outliers by plotting the resuduals

performance::check_model(model_main_effects4, detrend = FALSE)

Overall, the model shows a generally good fit with some concerns:

fit model onto the plot

# Get fitted values directly from the model
fitted_values <- predict(model_main_effects4, re.form = NA)  

# Exponentiate the fitted values to transform back to the original scale
filtered_data$fitted <- exp(fitted_values)

# Now create your plot with a caption at the bottom
plot <- ggplot(filtered_data, aes(x = species, y = SLA, fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = fitted), position = position_dodge(width = 0.75), color = "brown", size = 1.5) +  # Use exponentiated fitted values
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(
    axis.text.x = element_text(angle = 90, hjust = 1),
    plot.margin = unit(c(1, 1, 2, 1), "lines"),  
    plot.caption = element_text(hjust = 0.5)  
  ) +
  labs(
    title = "SLA vs Treatment by Species",
    x = "Species", y = "SLA", 
    caption = "Figure 1: Shows SLA of the four species under ambient and extreme drought conditions in two distinct successional phases (pioneer and mature) and two distinct sites (Tjøtta in the north and Lygra in the south)."
  ) +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

print(plot)

Interaction models for SLA

#species * droughtTrt
sla_species_droughtTrt <- lmer(log(SLA) ~ species * DroughtTrt + 
                                       (1 | DroughNet_plotID/plant_nr), data = 
                                       filtered_data)
summary(sla_species_droughtTrt)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ species * DroughtTrt + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: -131.8

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.3572 -0.5835 -0.0825  0.5425  3.4109 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.005079 0.07126 
 DroughNet_plotID          (Intercept) 0.007169 0.08467 
 Residual                              0.041850 0.20457 
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                                 Estimate Std. Error        df
(Intercept)                                       4.25051    0.03375  39.07141
speciesEmpetrum nigrum                            0.44237    0.02956 725.94363
speciesVaccinium myrtillus                        1.19256    0.02979 695.88835
speciesVaccinium vitis-idaea                      0.51377    0.02932 692.46300
DroughtTrtExt (90)                                0.04197    0.04770  38.97447
speciesEmpetrum nigrum:DroughtTrtExt (90)         0.02792    0.04208 719.20686
speciesVaccinium myrtillus:DroughtTrtExt (90)    -0.12420    0.04390 697.24289
speciesVaccinium vitis-idaea:DroughtTrtExt (90)  -0.11427    0.04092 692.44766
                                                t value Pr(>|t|)    
(Intercept)                                     125.959  < 2e-16 ***
speciesEmpetrum nigrum                           14.965  < 2e-16 ***
speciesVaccinium myrtillus                       40.035  < 2e-16 ***
speciesVaccinium vitis-idaea                     17.523  < 2e-16 ***
DroughtTrtExt (90)                                0.880  0.38423    
speciesEmpetrum nigrum:DroughtTrtExt (90)         0.664  0.50720    
speciesVaccinium myrtillus:DroughtTrtExt (90)    -2.829  0.00480 ** 
speciesVaccinium vitis-idaea:DroughtTrtExt (90)  -2.793  0.00537 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) spcsEn spcsVm spcVv- DTE(90 sEn:D( sVm:D(
spcsEmptrmn -0.421                                          
spcsVccnmmy -0.406  0.473                                   
spcsVccvts- -0.413  0.474  0.467                            
DrghtTE(90) -0.708  0.298  0.287  0.292                     
sEn:DTE(90)  0.296 -0.703 -0.332 -0.333 -0.414              
sVm:DTE(90)  0.275 -0.321 -0.679 -0.317 -0.388  0.461       
sVv-:DTE(90  0.296 -0.340 -0.335 -0.717 -0.419  0.475  0.453
performance::check_model(sla_species_droughtTrt, detrend = FALSE)

In summary, the model seems to have a good fit overall. high VIF for the ‘species:DroughtTrt’ interaction term is acceptable, and slight deviations from normality in the residuals. As for the residuals, the minor deviations from normality .

# Get fitted values directly from the model
fitted_values <- predict(sla_species_droughtTrt, re.form = NA)  # 'NA' to exclude random effects

# Add the fitted values to the filtered_data dataframe
filtered_data$fitted <- fitted_values  # Corrected .fitted to fitted


plot <- ggplot(filtered_data, aes(x = species, y = log(SLA), fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = fitted), position = position_dodge(width = 0.75), color = "brown", size = 1.5) +
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(
    axis.text.x = element_text(angle = 90, hjust = 1),
    plot.margin = unit(c(1, 1, 2, 1), "lines"),  
    plot.caption = element_text(hjust = 0.5)  # Center align the caption
  ) +
  labs(
    title = "SLA vs Treatment by Species",
    x = "Species", y = "SLA",
    caption = "Figure 1: Shows SLA of the four species under ambient and extreme drought conditions in two distinct successional phases (pioneer nad Mature) and two distinct sites (Tjøtta in the north and Lygra in the south)."
  ) +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))


print(plot)

#species * ageclass
sla_species_ageClass <- lmer(log(SLA) ~ species * ageClass + 
                                        (1 | DroughNet_plotID), data =   
                                        filtered_data)

summary(sla_species_ageClass)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ species * ageClass + (1 | DroughNet_plotID)
   Data: filtered_data

REML criterion at convergence: -114.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.1156 -0.5935 -0.0548  0.4972  3.2535 

Random effects:
 Groups           Name        Variance Std.Dev.
 DroughNet_plotID (Intercept) 0.007431 0.0862  
 Residual                     0.045507 0.2133  
Number of obs: 765, groups:  DroughNet_plotID, 24

Fixed effects:
                                              Estimate Std. Error        df
(Intercept)                                    4.31744    0.03245  44.37571
speciesEmpetrum nigrum                         0.39842    0.03198 747.91799
speciesVaccinium myrtillus                     1.14731    0.03203 745.95011
speciesVaccinium vitis-idaea                   0.47229    0.02924 735.34994
ageClassPioneer                               -0.07719    0.04599  44.75338
speciesEmpetrum nigrum:ageClassPioneer         0.08786    0.04345 743.47898
speciesVaccinium myrtillus:ageClassPioneer    -0.03148    0.04519 744.60684
speciesVaccinium vitis-idaea:ageClassPioneer  -0.05013    0.04237 736.82365
                                             t value Pr(>|t|)    
(Intercept)                                  133.055   <2e-16 ***
speciesEmpetrum nigrum                        12.460   <2e-16 ***
speciesVaccinium myrtillus                    35.824   <2e-16 ***
speciesVaccinium vitis-idaea                  16.152   <2e-16 ***
ageClassPioneer                               -1.678   0.1003    
speciesEmpetrum nigrum:ageClassPioneer         2.022   0.0435 *  
speciesVaccinium myrtillus:ageClassPioneer    -0.697   0.4863    
speciesVaccinium vitis-idaea:ageClassPioneer  -1.183   0.2371    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) spcsEn spcsVm spcVv- agClsP sEn:CP sVm:CP
spcsEmptrmn -0.418                                          
spcsVccnmmy -0.416  0.450                                   
spcsVccvts- -0.457  0.464  0.462                            
ageClassPnr -0.706  0.295  0.294  0.322                     
spcsEngr:CP  0.308 -0.736 -0.331 -0.342 -0.439              
spcsVmyr:CP  0.295 -0.319 -0.709 -0.327 -0.420  0.461       
spcsVvt-:CP  0.315 -0.320 -0.319 -0.690 -0.450  0.474  0.453
performance::check_model(sla_species_ageClass, detrend = FALSE)

# Get fitted values directly from the model
fitted_values <- predict(sla_species_ageClass, re.form = NA)  # 'NA' to exclude random effects

# Add the fitted values to the filtered_data dataframe
filtered_data$fitted <- exp(fitted_values)  # Corrected .fitted to fitted


plot <- ggplot(filtered_data, aes(x = species, y = SLA, fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = fitted), position = position_dodge(width = 0.75), color = "brown", size = 1.5) +
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(
    axis.text.x = element_text(angle = 90, hjust = 1),
    plot.margin = unit(c(1, 1, 2, 1), "lines"),  
    plot.caption = element_text(hjust = 0.5) 
  ) +
  labs(
    title = "SLA vs Treatment by Species",
    x = "Species", y = "SLA",
    caption = "Figure 1: Shows SLA of the four species under ambient and extreme drought conditions in two distinct successional phases (pioneer nad Mature) and two distinct sites (Tjøtta in the north and Lygra in the south)."
  ) +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

# Print the plot
print(plot)

# species * siteID
sla_species_siteID <- lmer(log(SLA) ~ species * siteID + 
                                      (1 | DroughNet_plotID), data = 
                                      filtered_data)

summary(sla_species_siteID)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ species * siteID + (1 | DroughNet_plotID)
   Data: filtered_data

REML criterion at convergence: -153.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.8127 -0.5784 -0.0517  0.5263  3.3217 

Random effects:
 Groups           Name        Variance Std.Dev.
 DroughNet_plotID (Intercept) 0.004578 0.06766 
 Residual                     0.043666 0.20896 
Number of obs: 765, groups:  DroughNet_plotID, 24

Fixed effects:
                                           Estimate Std. Error        df
(Intercept)                                 4.30581    0.02861  58.33859
speciesEmpetrum nigrum                      0.43005    0.03168 754.09060
speciesVaccinium myrtillus                  1.16166    0.03258 751.05284
speciesVaccinium vitis-idaea                0.57441    0.03024 739.17435
siteIDTjøtta                               -0.05570    0.04006  56.13847
speciesEmpetrum nigrum:siteIDTjøtta         0.02295    0.04258 747.84125
speciesVaccinium myrtillus:siteIDTjøtta    -0.06125    0.04436 747.92330
speciesVaccinium vitis-idaea:siteIDTjøtta  -0.23071    0.04152 737.49954
                                          t value Pr(>|t|)    
(Intercept)                               150.506  < 2e-16 ***
speciesEmpetrum nigrum                     13.575  < 2e-16 ***
speciesVaccinium myrtillus                 35.653  < 2e-16 ***
speciesVaccinium vitis-idaea               18.998  < 2e-16 ***
siteIDTjøtta                               -1.390    0.170    
speciesEmpetrum nigrum:siteIDTjøtta         0.539    0.590    
speciesVaccinium myrtillus:siteIDTjøtta    -1.381    0.168    
speciesVaccinium vitis-idaea:siteIDTjøtta  -5.557 3.83e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning in abbreviate(rn, minlength = 11): abbreviate used with non-ASCII chars

Correlation of Fixed Effects:
Warning in abbreviate(rn, minlength = 6): abbreviate used with non-ASCII chars
            (Intr) spcsEn spcsVm spcVv- stIDTj sEn:ID sVm:ID
spcsEmptrmn -0.484                                          
spcsVccnmmy -0.469  0.454                                   
spcsVccvts- -0.505  0.446  0.435                            
siteIDTjøtt -0.714  0.346  0.335  0.360                     
spcsEng:IDT  0.360 -0.744 -0.337 -0.332 -0.495              
spcsVmy:IDT  0.345 -0.333 -0.735 -0.319 -0.473  0.461       
spcsVv-:IDT  0.368 -0.325 -0.317 -0.728 -0.506  0.471  0.451
performance::check_model(sla_species_siteID, detrend = FALSE)

# Get fitted values directly from the model
fitted_values <- predict(sla_species_siteID, re.form = NA)  # 'NA' to exclude random effects


filtered_data$fitted <- fitted_values  # Corrected .fitted to fitted


plot <- ggplot(filtered_data, aes(x = species, y = log(SLA), fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = fitted), position = position_dodge(width = 0.75), color = "brown", size = 1.5) +
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(
    axis.text.x = element_text(angle = 90, hjust = 1),
    plot.margin = unit(c(1, 1, 2, 1), "lines"), 
    plot.caption = element_text(hjust = 0.5)  # Center align the caption
  ) +
  labs(
    title = "SLA vs Treatment by Species",
    x = "Species", y = "SLA",
    caption = "Figure 1: Shows SLA of the four species under ambient and extreme drought conditions in two distinct successional phases (pioneer nad Mature) and two distinct sites (Tjøtta in the north and Lygra in the south)."
  ) +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

# Print the plot
print(plot)

model_three_interactions <- lmer(log(SLA) ~ (species + DroughtTrt + ageClass +  siteID)^3 +
                                        (1 | DroughNet_plotID/plant_nr),
                           data = filtered_data)
summary(model_three_interactions)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ (species + DroughtTrt + ageClass + siteID)^3 + (1 |  
    DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: -152.6

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.9151 -0.5944 -0.0580  0.5476  3.1200 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.005768 0.07595 
 DroughNet_plotID          (Intercept) 0.000409 0.02022 
 Residual                              0.038134 0.19528 
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                                                 Estimate
(Intercept)                                                       4.33544
speciesEmpetrum nigrum                                            0.36062
speciesVaccinium myrtillus                                        1.21810
speciesVaccinium vitis-idaea                                      0.69812
DroughtTrtExt (90)                                                0.02931
ageClassPioneer                                                  -0.09278
siteIDTjøtta                                                     -0.17053
speciesEmpetrum nigrum:DroughtTrtExt (90)                         0.02499
speciesVaccinium myrtillus:DroughtTrtExt (90)                    -0.23990
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                  -0.19275
speciesEmpetrum nigrum:ageClassPioneer                            0.09904
speciesVaccinium myrtillus:ageClassPioneer                       -0.02672
speciesVaccinium vitis-idaea:ageClassPioneer                     -0.07386
speciesEmpetrum nigrum:siteIDTjøtta                               0.06078
speciesVaccinium myrtillus:siteIDTjøtta                           0.05321
speciesVaccinium vitis-idaea:siteIDTjøtta                        -0.28155
DroughtTrtExt (90):ageClassPioneer                               -0.05218
DroughtTrtExt (90):siteIDTjøtta                                   0.19211
ageClassPioneer:siteIDTjøtta                                      0.17491
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer         0.04106
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer     0.23658
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   0.08373
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta           -0.04898
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta       -0.02429
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.05029
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta              -0.03071
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta          -0.19982
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.03037
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -0.22165
                                                                Std. Error
(Intercept)                                                        0.04587
speciesEmpetrum nigrum                                             0.05886
speciesVaccinium myrtillus                                         0.05514
speciesVaccinium vitis-idaea                                       0.05060
DroughtTrtExt (90)                                                 0.06330
ageClassPioneer                                                    0.06301
siteIDTjøtta                                                       0.06232
speciesEmpetrum nigrum:DroughtTrtExt (90)                          0.07767
speciesVaccinium myrtillus:DroughtTrtExt (90)                      0.08410
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                    0.06688
speciesEmpetrum nigrum:ageClassPioneer                             0.07305
speciesVaccinium myrtillus:ageClassPioneer                         0.07185
speciesVaccinium vitis-idaea:ageClassPioneer                       0.07184
speciesEmpetrum nigrum:siteIDTjøtta                                0.07203
speciesVaccinium myrtillus:siteIDTjøtta                            0.07084
speciesVaccinium vitis-idaea:siteIDTjøtta                          0.06675
DroughtTrtExt (90):ageClassPioneer                                 0.08259
DroughtTrtExt (90):siteIDTjøtta                                    0.08231
ageClassPioneer:siteIDTjøtta                                       0.08246
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer          0.08117
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer      0.08684
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer    0.07877
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta             0.08162
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta         0.08746
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta       0.07881
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta                0.08223
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta            0.08669
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta          0.07896
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                    0.09699
                                                                       df
(Intercept)                                                      47.63988
speciesEmpetrum nigrum                                          677.71888
speciesVaccinium myrtillus                                      666.61804
speciesVaccinium vitis-idaea                                    657.73920
DroughtTrtExt (90)                                               43.45914
ageClassPioneer                                                  41.87801
siteIDTjøtta                                                     40.36221
speciesEmpetrum nigrum:DroughtTrtExt (90)                       693.80039
speciesVaccinium myrtillus:DroughtTrtExt (90)                   678.30705
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 661.08060
speciesEmpetrum nigrum:ageClassPioneer                          717.46779
speciesVaccinium myrtillus:ageClassPioneer                      682.27588
speciesVaccinium vitis-idaea:ageClassPioneer                    687.09493
speciesEmpetrum nigrum:siteIDTjøtta                             702.89385
speciesVaccinium myrtillus:siteIDTjøtta                         680.97864
speciesVaccinium vitis-idaea:siteIDTjøtta                       676.73154
DroughtTrtExt (90):ageClassPioneer                               31.01505
DroughtTrtExt (90):siteIDTjøtta                                  30.79044
ageClassPioneer:siteIDTjøtta                                     30.93959
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer       697.92635
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer   683.05511
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 680.40014
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta          707.53267
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta      683.75428
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    679.95628
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta             706.31437
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta         684.12962
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       682.13892
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  14.79742
                                                                t value
(Intercept)                                                      94.515
speciesEmpetrum nigrum                                            6.126
speciesVaccinium myrtillus                                       22.089
speciesVaccinium vitis-idaea                                     13.796
DroughtTrtExt (90)                                                0.463
ageClassPioneer                                                  -1.472
siteIDTjøtta                                                     -2.737
speciesEmpetrum nigrum:DroughtTrtExt (90)                         0.322
speciesVaccinium myrtillus:DroughtTrtExt (90)                    -2.852
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                  -2.882
speciesEmpetrum nigrum:ageClassPioneer                            1.356
speciesVaccinium myrtillus:ageClassPioneer                       -0.372
speciesVaccinium vitis-idaea:ageClassPioneer                     -1.028
speciesEmpetrum nigrum:siteIDTjøtta                               0.844
speciesVaccinium myrtillus:siteIDTjøtta                           0.751
speciesVaccinium vitis-idaea:siteIDTjøtta                        -4.218
DroughtTrtExt (90):ageClassPioneer                               -0.632
DroughtTrtExt (90):siteIDTjøtta                                   2.334
ageClassPioneer:siteIDTjøtta                                      2.121
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer         0.506
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer     2.724
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   1.063
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta           -0.600
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta       -0.278
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.638
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta              -0.373
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta          -2.305
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.385
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -2.285
                                                                Pr(>|t|)    
(Intercept)                                                      < 2e-16 ***
speciesEmpetrum nigrum                                          1.52e-09 ***
speciesVaccinium myrtillus                                       < 2e-16 ***
speciesVaccinium vitis-idaea                                     < 2e-16 ***
DroughtTrtExt (90)                                               0.64559    
ageClassPioneer                                                  0.14839    
siteIDTjøtta                                                     0.00919 ** 
speciesEmpetrum nigrum:DroughtTrtExt (90)                        0.74778    
speciesVaccinium myrtillus:DroughtTrtExt (90)                    0.00447 ** 
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                  0.00408 ** 
speciesEmpetrum nigrum:ageClassPioneer                           0.17559    
speciesVaccinium myrtillus:ageClassPioneer                       0.71011    
speciesVaccinium vitis-idaea:ageClassPioneer                     0.30428    
speciesEmpetrum nigrum:siteIDTjøtta                              0.39906    
speciesVaccinium myrtillus:siteIDTjøtta                          0.45285    
speciesVaccinium vitis-idaea:siteIDTjøtta                       2.80e-05 ***
DroughtTrtExt (90):ageClassPioneer                               0.53217    
DroughtTrtExt (90):siteIDTjøtta                                  0.02629 *  
ageClassPioneer:siteIDTjøtta                                     0.04203 *  
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer        0.61310    
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer    0.00661 ** 
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer  0.28819    
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta           0.54861    
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta       0.78131    
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta     0.52358    
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta              0.70893    
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta          0.02146 *  
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta        0.70068    
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  0.03749 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation matrix not shown by default, as p = 29 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
#validate model
performance::check_model(model_three_interactions, detrend = FALSE)

Trait 4- mean_thickness

#general model
#model with all the main effects
model_main_mean_thickness_effects <- lmer(mean_thickness ~ species + DroughtTrt + ageClass + siteID +
                           (1 | DroughNet_plotID/plant_nr),
                           data = filtered_data) 
summary(model_main_mean_thickness_effects )
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ species + DroughtTrt + ageClass + siteID + (1 |  
    DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: -1873.9

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.1179 -0.5755 -0.1043  0.3895  4.9624 

Random effects:
 Groups                    Name        Variance  Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.0001841 0.01357 
 DroughNet_plotID          (Intercept) 0.0001764 0.01328 
 Residual                              0.0044818 0.06695 
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                               Estimate Std. Error         df t value Pr(>|t|)
(Intercept)                   3.837e-01  8.906e-03  3.206e+01  43.087  < 2e-16
speciesEmpetrum nigrum       -2.059e-01  6.807e-03  7.302e+02 -30.250  < 2e-16
speciesVaccinium myrtillus   -2.862e-01  7.091e-03  7.146e+02 -40.358  < 2e-16
speciesVaccinium vitis-idaea -1.169e-01  6.659e-03  6.995e+02 -17.558  < 2e-16
DroughtTrtExt (90)           -7.296e-05  7.949e-03  2.021e+01  -0.009    0.993
ageClassPioneer               7.590e-04  7.961e-03  2.036e+01   0.095    0.925
siteIDTjøtta                  5.656e-02  7.952e-03  2.031e+01   7.113 6.23e-07
                                
(Intercept)                  ***
speciesEmpetrum nigrum       ***
speciesVaccinium myrtillus   ***
speciesVaccinium vitis-idaea ***
DroughtTrtExt (90)              
ageClassPioneer                 
siteIDTjøtta                 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning in abbreviate(rn, minlength = 11): abbreviate used with non-ASCII chars

Correlation of Fixed Effects:
Warning in abbreviate(rn, minlength = 6): abbreviate used with non-ASCII chars
            (Intr) spcsEn spcsVm spcVv- DTE(90 agClsP
spcsEmptrmn -0.335                                   
spcsVccnmmy -0.344  0.462                            
spcsVccvts- -0.363  0.477  0.457                     
DrghtTE(90) -0.432  0.014  0.032 -0.012              
ageClassPnr -0.454 -0.046 -0.013  0.013 -0.017       
siteIDTjøtt -0.462 -0.025 -0.016 -0.006 -0.015  0.038
performance::check_model(model_main_mean_thickness_effects ,  detrend = FALSE)

Overall, the model diagnostics suggest that the model fits well, with residuals that are mostly normally distributed and no major concerns with collinearity or influential outliers. However, there might be a slight issue with homoscedasticity, as indicated by the Homogeneity of Variance plot.

plot the model

# Get fitted values directly from the model
fitted_values <- predict(model_main_mean_thickness_effects , re.form = NA)  # 'NA' to exclude random effects

# Add the fitted values to the filtered_data dataframe
filtered_data$fitted <- fitted_values  #to fitted

plot <- ggplot(filtered_data, aes(x = species, y = mean_thickness, fill = DroughtTrt)) +
  geom_boxplot() +
  geom_point(aes(y = fitted), position = position_dodge(width = 0.75), color = "brown", size = 1.5) +
  facet_grid(ageClass ~ siteID, scales = "free") +
  theme_bw() +
  theme(
    axis.text.x = element_text(angle = 90, hjust = 1),
    plot.margin = unit(c(1, 1, 2, 1), "lines"),  
    plot.caption = element_text(hjust = 0.5)  # Center align the caption
  ) +
  labs(
    title = "SLA vs Treatment by Species",
    x = "Species", y = "mean_thickness",
    caption = "Figure 1: Shows mean_thickness of the four species under ambient and extreme drought conditions in two distinct successional phases (pioneer nad Mature) and two distinct sites (Tjøtta in the north and Lygra in the south)."
  ) +
  scale_fill_manual(values = c("Amb (0)" = "blue", "Ext (90)" = "grey"))

# Print the plot
print(plot)

interactions

# species * drought treatment
model_species_droughtTrt <- lmer(mean_thickness ~ species * DroughtTrt +
                                   (1 | DroughNet_plotID/plant_nr), 
                                 data = filtered_data)
            
summary(model_species_droughtTrt)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: 
mean_thickness ~ species * DroughtTrt + (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: -1842.6

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.1070 -0.5702 -0.0686  0.3895  5.0187 

Random effects:
 Groups                    Name        Variance  Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.0002640 0.01625 
 DroughNet_plotID          (Intercept) 0.0009873 0.03142 
 Residual                              0.0044530 0.06673 
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                                  Estimate Std. Error
(Intercept)                                       0.417433   0.011512
speciesEmpetrum nigrum                           -0.210307   0.009580
speciesVaccinium myrtillus                       -0.293721   0.009685
speciesVaccinium vitis-idaea                     -0.125226   0.009536
DroughtTrtExt (90)                               -0.009324   0.016273
speciesEmpetrum nigrum:DroughtTrtExt (90)         0.006745   0.013654
speciesVaccinium myrtillus:DroughtTrtExt (90)     0.015481   0.014283
speciesVaccinium vitis-idaea:DroughtTrtExt (90)   0.016143   0.013308
                                                        df t value Pr(>|t|)    
(Intercept)                                      36.603323  36.262   <2e-16 ***
speciesEmpetrum nigrum                          729.419269 -21.953   <2e-16 ***
speciesVaccinium myrtillus                      701.366546 -30.327   <2e-16 ***
speciesVaccinium vitis-idaea                    698.311636 -13.132   <2e-16 ***
DroughtTrtExt (90)                               36.539273  -0.573    0.570    
speciesEmpetrum nigrum:DroughtTrtExt (90)       722.887781   0.494    0.621    
speciesVaccinium myrtillus:DroughtTrtExt (90)   701.984099   1.084    0.279    
speciesVaccinium vitis-idaea:DroughtTrtExt (90) 697.021640   1.213    0.226    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) spcsEn spcsVm spcVv- DTE(90 sEn:D( sVm:D(
spcsEmptrmn -0.399                                          
spcsVccnmmy -0.387  0.473                                   
spcsVccvts- -0.394  0.473  0.466                            
DrghtTE(90) -0.707  0.283  0.274  0.279                     
sEn:DTE(90)  0.280 -0.702 -0.332 -0.332 -0.393              
sVm:DTE(90)  0.262 -0.321 -0.678 -0.316 -0.370  0.461       
sVv-:DTE(90  0.282 -0.339 -0.334 -0.717 -0.399  0.474  0.452
performance::check_model(model_species_droughtTrt, detrend = FALSE)

#species * ageclass
model_species_ageClass <- lmer(mean_thickness ~ species * ageClass +
                                    (1 | DroughNet_plotID), 
                                  data = filtered_data)
summary(model_species_ageClass)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ species * ageClass + (1 | DroughNet_plotID)
   Data: filtered_data

REML criterion at convergence: -1837.9

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0114 -0.5620 -0.0708  0.3776  5.1488 

Random effects:
 Groups           Name        Variance Std.Dev.
 DroughNet_plotID (Intercept) 0.001120 0.03347 
 Residual                     0.004626 0.06801 
Number of obs: 765, groups:  DroughNet_plotID, 24

Fixed effects:
                                               Estimate Std. Error         df
(Intercept)                                    0.410416   0.011723  36.264686
speciesEmpetrum nigrum                        -0.203529   0.010210 744.768359
speciesVaccinium myrtillus                    -0.289160   0.010224 743.188404
speciesVaccinium vitis-idaea                  -0.111190   0.009323 734.696244
ageClassPioneer                                0.002598   0.016608  36.510505
speciesEmpetrum nigrum:ageClassPioneer        -0.003788   0.013865 741.045649
speciesVaccinium myrtillus:ageClassPioneer     0.005632   0.014425 741.971661
speciesVaccinium vitis-idaea:ageClassPioneer  -0.009927   0.013511 735.789961
                                             t value Pr(>|t|)    
(Intercept)                                   35.009   <2e-16 ***
speciesEmpetrum nigrum                       -19.934   <2e-16 ***
speciesVaccinium myrtillus                   -28.283   <2e-16 ***
speciesVaccinium vitis-idaea                 -11.926   <2e-16 ***
ageClassPioneer                                0.156    0.877    
speciesEmpetrum nigrum:ageClassPioneer        -0.273    0.785    
speciesVaccinium myrtillus:ageClassPioneer     0.390    0.696    
speciesVaccinium vitis-idaea:ageClassPioneer  -0.735    0.463    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) spcsEn spcsVm spcVv- agClsP sEn:CP sVm:CP
spcsEmptrmn -0.369                                          
spcsVccnmmy -0.367  0.451                                   
spcsVccvts- -0.403  0.464  0.461                            
ageClassPnr -0.706  0.260  0.259  0.285                     
spcsEngr:CP  0.272 -0.736 -0.332 -0.341 -0.387              
spcsVmyr:CP  0.260 -0.320 -0.709 -0.327 -0.371  0.462       
spcsVvt-:CP  0.278 -0.320 -0.318 -0.690 -0.397  0.473  0.452
performance::check_model(model_species_ageClass, detrend = FALSE)

#species * ageclass
model_species_ageClass <- lmer(mean_thickness ~ species * ageClass +
                                    (1 | DroughNet_plotID), 
                                  data = filtered_data)
summary(model_species_ageClass)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ species * ageClass + (1 | DroughNet_plotID)
   Data: filtered_data

REML criterion at convergence: -1837.9

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0114 -0.5620 -0.0708  0.3776  5.1488 

Random effects:
 Groups           Name        Variance Std.Dev.
 DroughNet_plotID (Intercept) 0.001120 0.03347 
 Residual                     0.004626 0.06801 
Number of obs: 765, groups:  DroughNet_plotID, 24

Fixed effects:
                                               Estimate Std. Error         df
(Intercept)                                    0.410416   0.011723  36.264686
speciesEmpetrum nigrum                        -0.203529   0.010210 744.768359
speciesVaccinium myrtillus                    -0.289160   0.010224 743.188404
speciesVaccinium vitis-idaea                  -0.111190   0.009323 734.696244
ageClassPioneer                                0.002598   0.016608  36.510505
speciesEmpetrum nigrum:ageClassPioneer        -0.003788   0.013865 741.045649
speciesVaccinium myrtillus:ageClassPioneer     0.005632   0.014425 741.971661
speciesVaccinium vitis-idaea:ageClassPioneer  -0.009927   0.013511 735.789961
                                             t value Pr(>|t|)    
(Intercept)                                   35.009   <2e-16 ***
speciesEmpetrum nigrum                       -19.934   <2e-16 ***
speciesVaccinium myrtillus                   -28.283   <2e-16 ***
speciesVaccinium vitis-idaea                 -11.926   <2e-16 ***
ageClassPioneer                                0.156    0.877    
speciesEmpetrum nigrum:ageClassPioneer        -0.273    0.785    
speciesVaccinium myrtillus:ageClassPioneer     0.390    0.696    
speciesVaccinium vitis-idaea:ageClassPioneer  -0.735    0.463    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) spcsEn spcsVm spcVv- agClsP sEn:CP sVm:CP
spcsEmptrmn -0.369                                          
spcsVccnmmy -0.367  0.451                                   
spcsVccvts- -0.403  0.464  0.461                            
ageClassPnr -0.706  0.260  0.259  0.285                     
spcsEngr:CP  0.272 -0.736 -0.332 -0.341 -0.387              
spcsVmyr:CP  0.260 -0.320 -0.709 -0.327 -0.371  0.462       
spcsVvt-:CP  0.278 -0.320 -0.318 -0.690 -0.397  0.473  0.452
performance::check_model(model_species_ageClass, detrend = FALSE)

#species * siteID
model_species_siteID <- lmer(mean_thickness ~ species * siteID + 
                                  (1 | DroughNet_plotID), 
                                data = filtered_data)
summary(model_species_siteID)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ species * siteID + (1 | DroughNet_plotID)
   Data: filtered_data

REML criterion at convergence: -2109.5

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.6271 -0.5307 -0.0774  0.4006  5.3595 

Random effects:
 Groups           Name        Variance  Std.Dev.
 DroughNet_plotID (Intercept) 0.0001759 0.01326 
 Residual                     0.0033428 0.05782 
Number of obs: 765, groups:  DroughNet_plotID, 24

Fixed effects:
                                            Estimate Std. Error         df
(Intercept)                                 0.322980   0.006936  92.923731
speciesEmpetrum nigrum                     -0.118409   0.008718 756.909090
speciesVaccinium myrtillus                 -0.194467   0.008979 754.862118
speciesVaccinium vitis-idaea               -0.039256   0.008358 742.205970
siteIDTjøtta                                0.172673   0.009683  88.495156
speciesEmpetrum nigrum:siteIDTjøtta        -0.160886   0.011745 752.184026
speciesVaccinium myrtillus:siteIDTjøtta    -0.172138   0.012236 752.198981
speciesVaccinium vitis-idaea:siteIDTjøtta  -0.147249   0.011481 739.849185
                                          t value Pr(>|t|)    
(Intercept)                                46.567  < 2e-16 ***
speciesEmpetrum nigrum                    -13.582  < 2e-16 ***
speciesVaccinium myrtillus                -21.658  < 2e-16 ***
speciesVaccinium vitis-idaea               -4.697 3.15e-06 ***
siteIDTjøtta                               17.832  < 2e-16 ***
speciesEmpetrum nigrum:siteIDTjøtta       -13.698  < 2e-16 ***
speciesVaccinium myrtillus:siteIDTjøtta   -14.068  < 2e-16 ***
speciesVaccinium vitis-idaea:siteIDTjøtta -12.825  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning in abbreviate(rn, minlength = 11): abbreviate used with non-ASCII chars

Correlation of Fixed Effects:
Warning in abbreviate(rn, minlength = 6): abbreviate used with non-ASCII chars
            (Intr) spcsEn spcsVm spcVv- stIDTj sEn:ID sVm:ID
spcsEmptrmn -0.555                                          
spcsVccnmmy -0.538  0.450                                   
spcsVccvts- -0.577  0.451  0.439                            
siteIDTjøtt -0.716  0.397  0.385  0.413                     
spcsEng:IDT  0.412 -0.742 -0.334 -0.335 -0.567              
spcsVmy:IDT  0.395 -0.330 -0.734 -0.322 -0.543  0.460       
spcsVv-:IDT  0.420 -0.328 -0.320 -0.728 -0.580  0.474  0.454
#validate the model
performance::check_model(model_species_siteID, detrend = FALSE)

model_three_interactions <- lmer(mean_thickness ~ (species + DroughtTrt + ageClass +    siteID)^3 +
                                        (1 | DroughNet_plotID/plant_nr),
                                        data = filtered_data)
summary(model_three_interactions)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ (species + DroughtTrt + ageClass + siteID)^3 +  
    (1 | DroughNet_plotID/plant_nr)
   Data: filtered_data

REML criterion at convergence: -2037.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.3090 -0.5260 -0.0783  0.4249  5.5824 

Random effects:
 Groups                    Name        Variance  Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.0006618 0.02573 
 DroughNet_plotID          (Intercept) 0.0001715 0.01310 
 Residual                              0.0028506 0.05339 
Number of obs: 765, groups:  
plant_nr:DroughNet_plotID, 82; DroughNet_plotID, 24

Fixed effects:
                                                                  Estimate
(Intercept)                                                       0.303244
speciesEmpetrum nigrum                                           -0.077450
speciesVaccinium myrtillus                                       -0.158750
speciesVaccinium vitis-idaea                                     -0.016090
DroughtTrtExt (90)                                                0.001945
ageClassPioneer                                                   0.050475
siteIDTjøtta                                                      0.218180
speciesEmpetrum nigrum:DroughtTrtExt (90)                        -0.019649
speciesVaccinium myrtillus:DroughtTrtExt (90)                     0.012360
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.007446
speciesEmpetrum nigrum:ageClassPioneer                           -0.075153
speciesVaccinium myrtillus:ageClassPioneer                       -0.072692
speciesVaccinium vitis-idaea:ageClassPioneer                     -0.078264
speciesEmpetrum nigrum:siteIDTjøtta                              -0.230795
speciesVaccinium myrtillus:siteIDTjøtta                          -0.250140
speciesVaccinium vitis-idaea:siteIDTjøtta                        -0.199121
DroughtTrtExt (90):ageClassPioneer                               -0.007479
DroughtTrtExt (90):siteIDTjøtta                                  -0.015428
ageClassPioneer:siteIDTjøtta                                     -0.080589
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer         0.024414
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer     0.007371
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   0.022424
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta            0.032406
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta        0.020601
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta     -0.003360
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta               0.099772
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta           0.115135
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.112063
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -0.006039
                                                                Std. Error
(Intercept)                                                       0.015119
speciesEmpetrum nigrum                                            0.016350
speciesVaccinium myrtillus                                        0.015107
speciesVaccinium vitis-idaea                                      0.013849
DroughtTrtExt (90)                                                0.021062
ageClassPioneer                                                   0.020895
siteIDTjøtta                                                      0.020790
speciesEmpetrum nigrum:DroughtTrtExt (90)                         0.021500
speciesVaccinium myrtillus:DroughtTrtExt (90)                     0.023209
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.018311
speciesEmpetrum nigrum:ageClassPioneer                            0.020235
speciesVaccinium myrtillus:ageClassPioneer                        0.019715
speciesVaccinium vitis-idaea:ageClassPioneer                      0.019725
speciesEmpetrum nigrum:siteIDTjøtta                               0.019912
speciesVaccinium myrtillus:siteIDTjøtta                           0.019439
speciesVaccinium vitis-idaea:siteIDTjøtta                         0.018297
DroughtTrtExt (90):ageClassPioneer                                0.028123
DroughtTrtExt (90):siteIDTjøtta                                   0.028121
ageClassPioneer:siteIDTjøtta                                      0.028137
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer         0.022347
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer     0.023894
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   0.021605
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta            0.022511
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta        0.024071
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.021614
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta               0.022693
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta           0.023843
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.021662
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                   0.035647
                                                                        df
(Intercept)                                                      34.308254
speciesEmpetrum nigrum                                          711.210456
speciesVaccinium myrtillus                                      649.738978
speciesVaccinium vitis-idaea                                    642.380312
DroughtTrtExt (90)                                               32.134644
ageClassPioneer                                                  31.474807
siteIDTjøtta                                                     30.640162
speciesEmpetrum nigrum:DroughtTrtExt (90)                       702.540909
speciesVaccinium myrtillus:DroughtTrtExt (90)                   677.259898
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 645.897377
speciesEmpetrum nigrum:ageClassPioneer                          719.146736
speciesVaccinium myrtillus:ageClassPioneer                      664.766788
speciesVaccinium vitis-idaea:ageClassPioneer                    669.784049
speciesEmpetrum nigrum:siteIDTjøtta                             705.030164
speciesVaccinium myrtillus:siteIDTjøtta                         665.067635
speciesVaccinium vitis-idaea:siteIDTjøtta                       661.790848
DroughtTrtExt (90):ageClassPioneer                               25.720954
DroughtTrtExt (90):siteIDTjøtta                                  25.574021
ageClassPioneer:siteIDTjøtta                                     25.689805
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer       686.836281
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer   671.467461
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 665.063675
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta          699.576254
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta      672.180514
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    664.551718
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta             700.118109
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta         670.959026
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       666.921845
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  16.451792
                                                                t value
(Intercept)                                                      20.057
speciesEmpetrum nigrum                                           -4.737
speciesVaccinium myrtillus                                      -10.508
speciesVaccinium vitis-idaea                                     -1.162
DroughtTrtExt (90)                                                0.092
ageClassPioneer                                                   2.416
siteIDTjøtta                                                     10.494
speciesEmpetrum nigrum:DroughtTrtExt (90)                        -0.914
speciesVaccinium myrtillus:DroughtTrtExt (90)                     0.533
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.407
speciesEmpetrum nigrum:ageClassPioneer                           -3.714
speciesVaccinium myrtillus:ageClassPioneer                       -3.687
speciesVaccinium vitis-idaea:ageClassPioneer                     -3.968
speciesEmpetrum nigrum:siteIDTjøtta                             -11.591
speciesVaccinium myrtillus:siteIDTjøtta                         -12.868
speciesVaccinium vitis-idaea:siteIDTjøtta                       -10.883
DroughtTrtExt (90):ageClassPioneer                               -0.266
DroughtTrtExt (90):siteIDTjøtta                                  -0.549
ageClassPioneer:siteIDTjøtta                                     -2.864
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer         1.092
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer     0.308
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   1.038
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta            1.440
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta        0.856
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta     -0.155
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta               4.397
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta           4.829
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         5.173
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -0.169
                                                                Pr(>|t|)    
(Intercept)                                                      < 2e-16 ***
speciesEmpetrum nigrum                                          2.62e-06 ***
speciesVaccinium myrtillus                                       < 2e-16 ***
speciesVaccinium vitis-idaea                                    0.245745    
DroughtTrtExt (90)                                              0.926983    
ageClassPioneer                                                 0.021692 *  
siteIDTjøtta                                                    1.15e-11 ***
speciesEmpetrum nigrum:DroughtTrtExt (90)                       0.361076    
speciesVaccinium myrtillus:DroughtTrtExt (90)                   0.594518    
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 0.684417    
speciesEmpetrum nigrum:ageClassPioneer                          0.000220 ***
speciesVaccinium myrtillus:ageClassPioneer                      0.000245 ***
speciesVaccinium vitis-idaea:ageClassPioneer                    8.04e-05 ***
speciesEmpetrum nigrum:siteIDTjøtta                              < 2e-16 ***
speciesVaccinium myrtillus:siteIDTjøtta                          < 2e-16 ***
speciesVaccinium vitis-idaea:siteIDTjøtta                        < 2e-16 ***
DroughtTrtExt (90):ageClassPioneer                              0.792419    
DroughtTrtExt (90):siteIDTjøtta                                 0.588023    
ageClassPioneer:siteIDTjøtta                                    0.008219 ** 
speciesEmpetrum nigrum:DroughtTrtExt (90):ageClassPioneer       0.275006    
speciesVaccinium myrtillus:DroughtTrtExt (90):ageClassPioneer   0.757804    
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 0.299692    
speciesEmpetrum nigrum:DroughtTrtExt (90):siteIDTjøtta          0.150440    
speciesVaccinium myrtillus:DroughtTrtExt (90):siteIDTjøtta      0.392389    
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    0.876495    
speciesEmpetrum nigrum:ageClassPioneer:siteIDTjøtta             1.27e-05 ***
speciesVaccinium myrtillus:ageClassPioneer:siteIDTjøtta         1.70e-06 ***
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       3.05e-07 ***
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                 0.867546    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation matrix not shown by default, as p = 29 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
#validate model
performance::check_model(model_three_interactions, detrend = FALSE)

Analysis for leaf age (young and old leaves)

# Subset the data for the specified species with young and old leaves
subset_data <- subset(droughtnet_data2_clean, species %in% c("Vaccinium vitis-idaea", "Empetrum nigrum"))

# View the first few rows of the subsetted data
view(subset_data)

SLA

#1 sla
sla_leafAge <- lmer(log(SLA) ~ leaf_age + 
                            (1 | DroughNet_plotID/plant_nr), 
                          data = subset_data)
summary(sla_leafAge)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ leaf_age + (1 | DroughNet_plotID/plant_nr)
   Data: subset_data

REML criterion at convergence: -132.5

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.1907 -0.6009 -0.0195  0.5311  4.8100 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.004014 0.06336 
 DroughNet_plotID          (Intercept) 0.006329 0.07956 
 Residual                              0.044188 0.21021 
Number of obs: 791, groups:  
plant_nr:DroughNet_plotID, 78; DroughNet_plotID, 24

Fixed effects:
               Estimate Std. Error        df t value Pr(>|t|)    
(Intercept)     4.13704    0.02077  31.10155  199.21   <2e-16 ***
leaf_ageyoung   0.58574    0.01498 714.48193   39.11   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr)
leaf_ageyng -0.359
performance::check_model(sla_leafAge, detrend = FALSE)

sla_two_way_interactions <- lmer(log(SLA) ~ (species + leaf_age + DroughtTrt + ageClass + siteID)^2 +
                                (1 | DroughNet_plotID/plant_nr), 
                              data = subset_data)

summary(sla_two_way_interactions)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ (species + leaf_age + DroughtTrt + ageClass + siteID)^2 +  
    (1 | DroughNet_plotID/plant_nr)
   Data: subset_data

REML criterion at convergence: -185.8

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.0737 -0.5276 -0.0408  0.4293  5.3987 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.004134 0.06430 
 DroughNet_plotID          (Intercept) 0.006044 0.07774 
 Residual                              0.038264 0.19561 
Number of obs: 791, groups:  
plant_nr:DroughNet_plotID, 78; DroughNet_plotID, 24

Fixed effects:
                                                 Estimate Std. Error        df
(Intercept)                                       4.05860    0.05760  28.96998
speciesVaccinium vitis-idaea                      0.09942    0.03520 766.28616
leaf_ageyoung                                     0.71902    0.03327 706.10006
DroughtTrtExt (90)                                0.03967    0.07059  22.75539
ageClassPioneer                                   0.02104    0.06975  21.65696
siteIDTjøtta                                      0.06357    0.06988  21.90639
speciesVaccinium vitis-idaea:leaf_ageyoung        0.06328    0.02809 707.08954
speciesVaccinium vitis-idaea:DroughtTrtExt (90)  -0.05492    0.02930 759.62339
speciesVaccinium vitis-idaea:ageClassPioneer     -0.06970    0.02953 754.61224
speciesVaccinium vitis-idaea:siteIDTjøtta        -0.16614    0.03013 771.63037
leaf_ageyoung:DroughtTrtExt (90)                 -0.03271    0.02792 706.31626
leaf_ageyoung:ageClassPioneer                    -0.04005    0.02812 706.23519
leaf_ageyoung:siteIDTjøtta                       -0.23332    0.02807 706.77905
DroughtTrtExt (90):ageClassPioneer               -0.07652    0.07579  17.22791
DroughtTrtExt (90):siteIDTjøtta                   0.10575    0.07571  17.15349
ageClassPioneer:siteIDTjøtta                      0.09147    0.07603  17.42514
                                                t value Pr(>|t|)    
(Intercept)                                      70.457  < 2e-16 ***
speciesVaccinium vitis-idaea                      2.824  0.00486 ** 
leaf_ageyoung                                    21.614  < 2e-16 ***
DroughtTrtExt (90)                                0.562  0.57962    
ageClassPioneer                                   0.302  0.76575    
siteIDTjøtta                                      0.910  0.37289    
speciesVaccinium vitis-idaea:leaf_ageyoung        2.253  0.02458 *  
speciesVaccinium vitis-idaea:DroughtTrtExt (90)  -1.874  0.06127 .  
speciesVaccinium vitis-idaea:ageClassPioneer     -2.360  0.01851 *  
speciesVaccinium vitis-idaea:siteIDTjøtta        -5.515 4.77e-08 ***
leaf_ageyoung:DroughtTrtExt (90)                 -1.172  0.24178    
leaf_ageyoung:ageClassPioneer                    -1.424  0.15478    
leaf_ageyoung:siteIDTjøtta                       -8.311 4.86e-16 ***
DroughtTrtExt (90):ageClassPioneer               -1.010  0.32661    
DroughtTrtExt (90):siteIDTjøtta                   1.397  0.18029    
ageClassPioneer:siteIDTjøtta                      1.203  0.24502    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation matrix not shown by default, as p = 16 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
performance::check_model(sla_two_way_interactions, detrend = FALSE)

sla_three_way_interactions <- lmer(log(SLA) ~ (species + leaf_age + DroughtTrt + ageClass + siteID)^3 +
                                (1 | DroughNet_plotID/plant_nr), 
                              data = subset_data)

summary(sla_three_way_interactions)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ (species + leaf_age + DroughtTrt + ageClass + siteID)^3 +  
    (1 | DroughNet_plotID/plant_nr)
   Data: subset_data

REML criterion at convergence: -185.4

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.5260 -0.5459 -0.0158  0.4172  5.7494 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.004179 0.06464 
 DroughNet_plotID          (Intercept) 0.006670 0.08167 
 Residual                              0.036820 0.19189 
Number of obs: 791, groups:  
plant_nr:DroughNet_plotID, 78; DroughNet_plotID, 24

Fixed effects:
                                                                  Estimate
(Intercept)                                                       4.164321
speciesVaccinium vitis-idaea                                     -0.039070
leaf_ageyoung                                                     0.500145
DroughtTrtExt (90)                                               -0.033172
ageClassPioneer                                                  -0.060866
siteIDTjøtta                                                     -0.022097
speciesVaccinium vitis-idaea:leaf_ageyoung                        0.357743
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.031657
speciesVaccinium vitis-idaea:ageClassPioneer                      0.002418
speciesVaccinium vitis-idaea:siteIDTjøtta                        -0.079269
leaf_ageyoung:DroughtTrtExt (90)                                  0.135596
leaf_ageyoung:ageClassPioneer                                     0.118028
leaf_ageyoung:siteIDTjøtta                                       -0.045528
DroughtTrtExt (90):ageClassPioneer                               -0.040300
DroughtTrtExt (90):siteIDTjøtta                                   0.113398
ageClassPioneer:siteIDTjøtta                                      0.137826
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)    -0.214868
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer       -0.118619
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta          -0.214885
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer  -0.012315
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.041693
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta        -0.003760
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                 -0.066982
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                    -0.053125
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                       -0.090387
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -0.002265
                                                                Std. Error
(Intercept)                                                       0.068976
speciesVaccinium vitis-idaea                                      0.053132
leaf_ageyoung                                                     0.052586
DroughtTrtExt (90)                                                0.095626
ageClassPioneer                                                   0.089669
siteIDTjøtta                                                      0.089951
speciesVaccinium vitis-idaea:leaf_ageyoung                        0.058911
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.063825
speciesVaccinium vitis-idaea:ageClassPioneer                      0.061359
speciesVaccinium vitis-idaea:siteIDTjøtta                         0.059423
leaf_ageyoung:DroughtTrtExt (90)                                  0.060505
leaf_ageyoung:ageClassPioneer                                     0.058685
leaf_ageyoung:siteIDTjøtta                                        0.057974
DroughtTrtExt (90):ageClassPioneer                                0.120838
DroughtTrtExt (90):siteIDTjøtta                                   0.121928
ageClassPioneer:siteIDTjøtta                                      0.118866
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)     0.055233
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer        0.055824
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta           0.056214
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   0.058115
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.059469
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.059885
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                  0.055295
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                     0.055337
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                        0.056258
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                   0.157314
                                                                        df
(Intercept)                                                      36.320479
speciesVaccinium vitis-idaea                                    751.535797
leaf_ageyoung                                                   696.909975
DroughtTrtExt (90)                                               34.320815
ageClassPioneer                                                  26.769363
siteIDTjøtta                                                     27.225404
speciesVaccinium vitis-idaea:leaf_ageyoung                      698.537708
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 756.520797
speciesVaccinium vitis-idaea:ageClassPioneer                    763.387413
speciesVaccinium vitis-idaea:siteIDTjøtta                       746.335920
leaf_ageyoung:DroughtTrtExt (90)                                697.494323
leaf_ageyoung:ageClassPioneer                                   698.305752
leaf_ageyoung:siteIDTjøtta                                      696.884614
DroughtTrtExt (90):ageClassPioneer                               22.399880
DroughtTrtExt (90):siteIDTjøtta                                  23.289154
ageClassPioneer:siteIDTjøtta                                     21.077911
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)   698.096429
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer      697.903832
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta         699.695589
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 743.630366
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    761.400853
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       760.929990
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                697.178122
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                   698.008549
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                      698.740524
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  16.317395
                                                                t value
(Intercept)                                                      60.373
speciesVaccinium vitis-idaea                                     -0.735
leaf_ageyoung                                                     9.511
DroughtTrtExt (90)                                               -0.347
ageClassPioneer                                                  -0.679
siteIDTjøtta                                                     -0.246
speciesVaccinium vitis-idaea:leaf_ageyoung                        6.073
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.496
speciesVaccinium vitis-idaea:ageClassPioneer                      0.039
speciesVaccinium vitis-idaea:siteIDTjøtta                        -1.334
leaf_ageyoung:DroughtTrtExt (90)                                  2.241
leaf_ageyoung:ageClassPioneer                                     2.011
leaf_ageyoung:siteIDTjøtta                                       -0.785
DroughtTrtExt (90):ageClassPioneer                               -0.334
DroughtTrtExt (90):siteIDTjøtta                                   0.930
ageClassPioneer:siteIDTjøtta                                      1.160
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)    -3.890
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer       -2.125
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta          -3.823
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer  -0.212
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.701
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta        -0.063
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                 -1.211
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                    -0.960
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                       -1.607
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -0.014
                                                                Pr(>|t|)    
(Intercept)                                                      < 2e-16 ***
speciesVaccinium vitis-idaea                                    0.462364    
leaf_ageyoung                                                    < 2e-16 ***
DroughtTrtExt (90)                                              0.730791    
ageClassPioneer                                                 0.503098    
siteIDTjøtta                                                    0.807794    
speciesVaccinium vitis-idaea:leaf_ageyoung                      2.07e-09 ***
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 0.620035    
speciesVaccinium vitis-idaea:ageClassPioneer                    0.968576    
speciesVaccinium vitis-idaea:siteIDTjøtta                       0.182620    
leaf_ageyoung:DroughtTrtExt (90)                                0.025334 *  
leaf_ageyoung:ageClassPioneer                                   0.044689 *  
leaf_ageyoung:siteIDTjøtta                                      0.432531    
DroughtTrtExt (90):ageClassPioneer                              0.741857    
DroughtTrtExt (90):siteIDTjøtta                                 0.361891    
ageClassPioneer:siteIDTjøtta                                    0.259215    
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)   0.000110 ***
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer      0.033947 *  
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta         0.000144 ***
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 0.832233    
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    0.483458    
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       0.949958    
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                0.226170    
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                   0.337375    
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                      0.108586    
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                 0.988685    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation matrix not shown by default, as p = 26 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
performance::check_model(sla_three_way_interactions, detrend = FALSE)

LDMC

#2 ldmc
ldmc_leafAge <- lmer(LDMC ~ leaf_age + 
                            (1 | DroughNet_plotID/plant_nr), 
                          data = subset_data)
summary(ldmc_leafAge)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: LDMC ~ leaf_age + (1 | DroughNet_plotID/plant_nr)
   Data: subset_data

REML criterion at convergence: 8784.5

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.1917 -0.5529  0.0390  0.6102  4.9448 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept)   10.89   3.301  
 DroughNet_plotID          (Intercept)  637.97  25.258  
 Residual                              3729.21  61.067  
Number of obs: 791, groups:  
plant_nr:DroughNet_plotID, 78; DroughNet_plotID, 24

Fixed effects:
              Estimate Std. Error       df t value Pr(>|t|)    
(Intercept)    475.886      6.030   30.779   78.92   <2e-16 ***
leaf_ageyoung -117.444      4.347  714.374  -27.02   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr)
leaf_ageyng -0.359
performance::check_model(ldmc_leafAge, detrend = FALSE)

ldmc_two_way_interactions <- lmer(LDMC ~ (species + leaf_age + DroughtTrt + ageClass + siteID)^2 +
                                (1 | DroughNet_plotID/plant_nr), 
                              data = subset_data)

summary(ldmc_two_way_interactions)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: LDMC ~ (species + leaf_age + DroughtTrt + ageClass + siteID)^2 +  
    (1 | DroughNet_plotID/plant_nr)
   Data: subset_data

REML criterion at convergence: 8452.6

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.7633 -0.5095  0.0196  0.5607  5.3078 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept)   54.6    7.389  
 DroughNet_plotID          (Intercept)  420.5   20.507  
 Residual                              2763.5   52.569  
Number of obs: 791, groups:  
plant_nr:DroughNet_plotID, 78; DroughNet_plotID, 24

Fixed effects:
                                                 Estimate Std. Error        df
(Intercept)                                      531.8178    14.5482   32.1346
speciesVaccinium vitis-idaea                     -43.7281     9.3175  772.4590
leaf_ageyoung                                   -150.2220     8.9329  710.7569
DroughtTrtExt (90)                               -15.5844    17.6431   24.2311
ageClassPioneer                                    3.0870    17.4679   23.3161
siteIDTjøtta                                     -87.4013    17.4453   23.2429
speciesVaccinium vitis-idaea:leaf_ageyoung       -49.4931     7.5413  712.0460
speciesVaccinium vitis-idaea:DroughtTrtExt (90)   27.6897     7.7714  767.8100
speciesVaccinium vitis-idaea:ageClassPioneer      13.3141     7.8460  763.9398
speciesVaccinium vitis-idaea:siteIDTjøtta         74.0447     7.9469  773.6796
leaf_ageyoung:DroughtTrtExt (90)                   6.3600     7.4977  710.7344
leaf_ageyoung:ageClassPioneer                     19.8013     7.5508  710.6576
leaf_ageyoung:siteIDTjøtta                        80.6202     7.5377  711.3683
DroughtTrtExt (90):ageClassPioneer                -0.2627    18.7626   17.6924
DroughtTrtExt (90):siteIDTjøtta                  -12.3720    18.7457   17.6445
ageClassPioneer:siteIDTjøtta                     -22.6797    18.8280   17.9239
                                                t value Pr(>|t|)    
(Intercept)                                      36.556  < 2e-16 ***
speciesVaccinium vitis-idaea                     -4.693 3.18e-06 ***
leaf_ageyoung                                   -16.817  < 2e-16 ***
DroughtTrtExt (90)                               -0.883 0.385746    
ageClassPioneer                                   0.177 0.861253    
siteIDTjøtta                                     -5.010 4.42e-05 ***
speciesVaccinium vitis-idaea:leaf_ageyoung       -6.563 1.02e-10 ***
speciesVaccinium vitis-idaea:DroughtTrtExt (90)   3.563 0.000389 ***
speciesVaccinium vitis-idaea:ageClassPioneer      1.697 0.090115 .  
speciesVaccinium vitis-idaea:siteIDTjøtta         9.317  < 2e-16 ***
leaf_ageyoung:DroughtTrtExt (90)                  0.848 0.396581    
leaf_ageyoung:ageClassPioneer                     2.622 0.008918 ** 
leaf_ageyoung:siteIDTjøtta                       10.696  < 2e-16 ***
DroughtTrtExt (90):ageClassPioneer               -0.014 0.988987    
DroughtTrtExt (90):siteIDTjøtta                  -0.660 0.517782    
ageClassPioneer:siteIDTjøtta                     -1.205 0.244034    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation matrix not shown by default, as p = 16 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
performance::check_model(ldmc_two_way_interactions, detrend = FALSE)

ldmc_three_way_interactions <- lmer(log(SLA) ~ (species + leaf_age + DroughtTrt + ageClass + siteID)^3 +
                                (1 | DroughNet_plotID/plant_nr), 
                              data = subset_data)

summary(ldmc_three_way_interactions)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ (species + leaf_age + DroughtTrt + ageClass + siteID)^3 +  
    (1 | DroughNet_plotID/plant_nr)
   Data: subset_data

REML criterion at convergence: -185.4

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.5260 -0.5459 -0.0158  0.4172  5.7494 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.004179 0.06464 
 DroughNet_plotID          (Intercept) 0.006670 0.08167 
 Residual                              0.036820 0.19189 
Number of obs: 791, groups:  
plant_nr:DroughNet_plotID, 78; DroughNet_plotID, 24

Fixed effects:
                                                                  Estimate
(Intercept)                                                       4.164321
speciesVaccinium vitis-idaea                                     -0.039070
leaf_ageyoung                                                     0.500145
DroughtTrtExt (90)                                               -0.033172
ageClassPioneer                                                  -0.060866
siteIDTjøtta                                                     -0.022097
speciesVaccinium vitis-idaea:leaf_ageyoung                        0.357743
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.031657
speciesVaccinium vitis-idaea:ageClassPioneer                      0.002418
speciesVaccinium vitis-idaea:siteIDTjøtta                        -0.079269
leaf_ageyoung:DroughtTrtExt (90)                                  0.135596
leaf_ageyoung:ageClassPioneer                                     0.118028
leaf_ageyoung:siteIDTjøtta                                       -0.045528
DroughtTrtExt (90):ageClassPioneer                               -0.040300
DroughtTrtExt (90):siteIDTjøtta                                   0.113398
ageClassPioneer:siteIDTjøtta                                      0.137826
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)    -0.214868
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer       -0.118619
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta          -0.214885
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer  -0.012315
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.041693
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta        -0.003760
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                 -0.066982
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                    -0.053125
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                       -0.090387
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -0.002265
                                                                Std. Error
(Intercept)                                                       0.068976
speciesVaccinium vitis-idaea                                      0.053132
leaf_ageyoung                                                     0.052586
DroughtTrtExt (90)                                                0.095626
ageClassPioneer                                                   0.089669
siteIDTjøtta                                                      0.089951
speciesVaccinium vitis-idaea:leaf_ageyoung                        0.058911
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.063825
speciesVaccinium vitis-idaea:ageClassPioneer                      0.061359
speciesVaccinium vitis-idaea:siteIDTjøtta                         0.059423
leaf_ageyoung:DroughtTrtExt (90)                                  0.060505
leaf_ageyoung:ageClassPioneer                                     0.058685
leaf_ageyoung:siteIDTjøtta                                        0.057974
DroughtTrtExt (90):ageClassPioneer                                0.120838
DroughtTrtExt (90):siteIDTjøtta                                   0.121928
ageClassPioneer:siteIDTjøtta                                      0.118866
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)     0.055233
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer        0.055824
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta           0.056214
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   0.058115
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.059469
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.059885
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                  0.055295
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                     0.055337
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                        0.056258
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                   0.157314
                                                                        df
(Intercept)                                                      36.320479
speciesVaccinium vitis-idaea                                    751.535797
leaf_ageyoung                                                   696.909975
DroughtTrtExt (90)                                               34.320815
ageClassPioneer                                                  26.769363
siteIDTjøtta                                                     27.225404
speciesVaccinium vitis-idaea:leaf_ageyoung                      698.537708
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 756.520797
speciesVaccinium vitis-idaea:ageClassPioneer                    763.387413
speciesVaccinium vitis-idaea:siteIDTjøtta                       746.335920
leaf_ageyoung:DroughtTrtExt (90)                                697.494323
leaf_ageyoung:ageClassPioneer                                   698.305752
leaf_ageyoung:siteIDTjøtta                                      696.884614
DroughtTrtExt (90):ageClassPioneer                               22.399880
DroughtTrtExt (90):siteIDTjøtta                                  23.289154
ageClassPioneer:siteIDTjøtta                                     21.077911
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)   698.096429
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer      697.903832
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta         699.695589
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 743.630366
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    761.400853
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       760.929990
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                697.178122
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                   698.008549
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                      698.740524
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  16.317395
                                                                t value
(Intercept)                                                      60.373
speciesVaccinium vitis-idaea                                     -0.735
leaf_ageyoung                                                     9.511
DroughtTrtExt (90)                                               -0.347
ageClassPioneer                                                  -0.679
siteIDTjøtta                                                     -0.246
speciesVaccinium vitis-idaea:leaf_ageyoung                        6.073
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.496
speciesVaccinium vitis-idaea:ageClassPioneer                      0.039
speciesVaccinium vitis-idaea:siteIDTjøtta                        -1.334
leaf_ageyoung:DroughtTrtExt (90)                                  2.241
leaf_ageyoung:ageClassPioneer                                     2.011
leaf_ageyoung:siteIDTjøtta                                       -0.785
DroughtTrtExt (90):ageClassPioneer                               -0.334
DroughtTrtExt (90):siteIDTjøtta                                   0.930
ageClassPioneer:siteIDTjøtta                                      1.160
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)    -3.890
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer       -2.125
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta          -3.823
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer  -0.212
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.701
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta        -0.063
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                 -1.211
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                    -0.960
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                       -1.607
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -0.014
                                                                Pr(>|t|)    
(Intercept)                                                      < 2e-16 ***
speciesVaccinium vitis-idaea                                    0.462364    
leaf_ageyoung                                                    < 2e-16 ***
DroughtTrtExt (90)                                              0.730791    
ageClassPioneer                                                 0.503098    
siteIDTjøtta                                                    0.807794    
speciesVaccinium vitis-idaea:leaf_ageyoung                      2.07e-09 ***
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 0.620035    
speciesVaccinium vitis-idaea:ageClassPioneer                    0.968576    
speciesVaccinium vitis-idaea:siteIDTjøtta                       0.182620    
leaf_ageyoung:DroughtTrtExt (90)                                0.025334 *  
leaf_ageyoung:ageClassPioneer                                   0.044689 *  
leaf_ageyoung:siteIDTjøtta                                      0.432531    
DroughtTrtExt (90):ageClassPioneer                              0.741857    
DroughtTrtExt (90):siteIDTjøtta                                 0.361891    
ageClassPioneer:siteIDTjøtta                                    0.259215    
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)   0.000110 ***
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer      0.033947 *  
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta         0.000144 ***
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 0.832233    
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    0.483458    
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       0.949958    
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                0.226170    
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                   0.337375    
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                      0.108586    
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                 0.988685    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation matrix not shown by default, as p = 26 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
performance::check_model(ldmc_three_way_interactions, detrend = FALSE)

mean thickness

species_leafAge <- lmer(mean_thickness ~ species * leaf_age + 
                                (1 | DroughNet_plotID/plant_nr), 
                              data = subset_data)

summary(species_leafAge)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ species * leaf_age + (1 | DroughNet_plotID/plant_nr)
   Data: subset_data

REML criterion at convergence: -2418.8

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0709 -0.5972 -0.0550  0.5213  4.2709 

Random effects:
 Groups                    Name        Variance  Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 1.127e-03 0.033576
 DroughNet_plotID          (Intercept) 8.708e-05 0.009331
 Residual                              2.201e-03 0.046914
Number of obs: 791, groups:  
plant_nr:DroughNet_plotID, 78; DroughNet_plotID, 24

Fixed effects:
                                             Estimate Std. Error         df
(Intercept)                                  0.285818   0.005522  43.162082
speciesVaccinium vitis-idaea                 0.081120   0.004856 730.122990
leaf_ageyoung                               -0.075433   0.004804 705.957281
speciesVaccinium vitis-idaea:leaf_ageyoung   0.007141   0.006696 706.640445
                                           t value Pr(>|t|)    
(Intercept)                                 51.760   <2e-16 ***
speciesVaccinium vitis-idaea                16.704   <2e-16 ***
leaf_ageyoung                              -15.702   <2e-16 ***
speciesVaccinium vitis-idaea:leaf_ageyoung   1.066    0.287    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) spcVv- lf_gyn
spcsVccvts- -0.463              
leaf_ageyng -0.437  0.497       
spcsVvts-:_  0.311 -0.682 -0.718
performance::check_model(species_leafAge, detrend = FALSE)

thickness_two_way_interactions <- lmer(mean_thickness ~ (species + leaf_age + DroughtTrt + ageClass + siteID)^2 +
                                (1 | DroughNet_plotID/plant_nr), 
                              data = subset_data)

summary(thickness_two_way_interactions)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ (species + leaf_age + DroughtTrt + ageClass +  
    siteID)^2 + (1 | DroughNet_plotID/plant_nr)
   Data: subset_data

REML criterion at convergence: -2342

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.8811 -0.5803 -0.0579  0.5515  4.2512 

Random effects:
 Groups                    Name        Variance  Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.0010775 0.03283 
 DroughNet_plotID          (Intercept) 0.0001851 0.01361 
 Residual                              0.0021966 0.04687 
Number of obs: 791, groups:  
plant_nr:DroughNet_plotID, 78; DroughNet_plotID, 24

Fixed effects:
                                                  Estimate Std. Error
(Intercept)                                      2.861e-01  1.476e-02
speciesVaccinium vitis-idaea                     7.618e-02  8.589e-03
leaf_ageyoung                                   -7.414e-02  7.977e-03
DroughtTrtExt (90)                              -1.967e-02  1.841e-02
ageClassPioneer                                 -1.102e-02  1.798e-02
siteIDTjøtta                                     2.340e-02  1.825e-02
speciesVaccinium vitis-idaea:leaf_ageyoung       6.288e-03  6.737e-03
speciesVaccinium vitis-idaea:DroughtTrtExt (90)  8.677e-03  7.128e-03
speciesVaccinium vitis-idaea:ageClassPioneer     9.771e-03  7.169e-03
speciesVaccinium vitis-idaea:siteIDTjøtta       -6.418e-03  7.387e-03
leaf_ageyoung:DroughtTrtExt (90)                 1.051e-02  6.695e-03
leaf_ageyoung:ageClassPioneer                   -5.587e-03  6.743e-03
leaf_ageyoung:siteIDTjøtta                      -5.701e-03  6.733e-03
DroughtTrtExt (90):ageClassPioneer               8.843e-03  1.993e-02
DroughtTrtExt (90):siteIDTjøtta                  1.826e-03  1.990e-02
ageClassPioneer:siteIDTjøtta                     3.538e-04  1.999e-02
                                                        df t value Pr(>|t|)    
(Intercept)                                      2.684e+01  19.381   <2e-16 ***
speciesVaccinium vitis-idaea                     7.452e+02   8.869   <2e-16 ***
leaf_ageyoung                                    6.991e+02  -9.294   <2e-16 ***
DroughtTrtExt (90)                               2.278e+01  -1.069    0.296    
ageClassPioneer                                  2.046e+01  -0.613    0.547    
siteIDTjøtta                                     2.204e+01   1.282    0.213    
speciesVaccinium vitis-idaea:leaf_ageyoung       6.996e+02   0.933    0.351    
speciesVaccinium vitis-idaea:DroughtTrtExt (90)  7.368e+02   1.217    0.224    
speciesVaccinium vitis-idaea:ageClassPioneer     7.326e+02   1.363    0.173    
speciesVaccinium vitis-idaea:siteIDTjøtta        7.519e+02  -0.869    0.385    
leaf_ageyoung:DroughtTrtExt (90)                 6.993e+02   1.570    0.117    
leaf_ageyoung:ageClassPioneer                    6.992e+02  -0.829    0.408    
leaf_ageyoung:siteIDTjøtta                       6.995e+02  -0.847    0.397    
DroughtTrtExt (90):ageClassPioneer               1.783e+01   0.444    0.663    
DroughtTrtExt (90):siteIDTjøtta                  1.770e+01   0.092    0.928    
ageClassPioneer:siteIDTjøtta                     1.803e+01   0.018    0.986    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation matrix not shown by default, as p = 16 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
performance::check_model(thickness_two_way_interactions, detrend = FALSE)

thickness_three_way_interactions <- lmer(mean_thickness ~ (species + leaf_age + DroughtTrt + ageClass + siteID)^3 +
                                (1 | DroughNet_plotID/plant_nr), 
                              data = subset_data)

summary(thickness_three_way_interactions)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ (species + leaf_age + DroughtTrt + ageClass +  
    siteID)^3 + (1 | DroughNet_plotID/plant_nr)
   Data: subset_data

REML criterion at convergence: -2296.5

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0030 -0.5602 -0.0661  0.4945  4.2021 

Random effects:
 Groups                    Name        Variance  Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.0010308 0.03211 
 DroughNet_plotID          (Intercept) 0.0002052 0.01433 
 Residual                              0.0021729 0.04661 
Number of obs: 791, groups:  
plant_nr:DroughNet_plotID, 78; DroughNet_plotID, 24

Fixed effects:
                                                                  Estimate
(Intercept)                                                       0.296835
speciesVaccinium vitis-idaea                                      0.062275
leaf_ageyoung                                                    -0.062086
DroughtTrtExt (90)                                               -0.049623
ageClassPioneer                                                  -0.024958
siteIDTjøtta                                                      0.011654
speciesVaccinium vitis-idaea:leaf_ageyoung                       -0.003298
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.039315
speciesVaccinium vitis-idaea:ageClassPioneer                      0.026674
speciesVaccinium vitis-idaea:siteIDTjøtta                         0.004515
leaf_ageyoung:DroughtTrtExt (90)                                  0.017594
leaf_ageyoung:ageClassPioneer                                    -0.015228
leaf_ageyoung:siteIDTjøtta                                       -0.034653
DroughtTrtExt (90):ageClassPioneer                                0.032877
DroughtTrtExt (90):siteIDTjøtta                                   0.043792
ageClassPioneer:siteIDTjøtta                                      0.020450
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)    -0.011394
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer       -0.011425
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta           0.036027
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer  -0.003307
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta     -0.036787
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta        -0.018187
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                  0.002563
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                    -0.001760
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                        0.021811
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -0.041161
                                                                Std. Error
(Intercept)                                                       0.017235
speciesVaccinium vitis-idaea                                      0.013101
leaf_ageyoung                                                     0.012784
DroughtTrtExt (90)                                                0.024209
ageClassPioneer                                                   0.022380
siteIDTjøtta                                                      0.022768
speciesVaccinium vitis-idaea:leaf_ageyoung                        0.014326
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   0.015765
speciesVaccinium vitis-idaea:ageClassPioneer                      0.015251
speciesVaccinium vitis-idaea:siteIDTjøtta                         0.014612
leaf_ageyoung:DroughtTrtExt (90)                                  0.014711
leaf_ageyoung:ageClassPioneer                                     0.014271
leaf_ageyoung:siteIDTjøtta                                        0.014093
DroughtTrtExt (90):ageClassPioneer                                0.030311
DroughtTrtExt (90):siteIDTjøtta                                   0.031189
ageClassPioneer:siteIDTjøtta                                      0.030155
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)     0.013431
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer        0.013573
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta           0.013674
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer   0.014290
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta      0.014765
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta         0.014849
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                  0.013443
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                     0.013456
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                        0.013682
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                   0.040187
                                                                        df
(Intercept)                                                      33.587838
speciesVaccinium vitis-idaea                                    731.176883
leaf_ageyoung                                                   690.300365
DroughtTrtExt (90)                                               34.042377
ageClassPioneer                                                  24.594952
siteIDTjøtta                                                     26.877818
speciesVaccinium vitis-idaea:leaf_ageyoung                      691.356915
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                 735.551165
speciesVaccinium vitis-idaea:ageClassPioneer                    745.539067
speciesVaccinium vitis-idaea:siteIDTjøtta                       727.798276
leaf_ageyoung:DroughtTrtExt (90)                                690.501843
leaf_ageyoung:ageClassPioneer                                   691.054187
leaf_ageyoung:siteIDTjøtta                                      690.257179
DroughtTrtExt (90):ageClassPioneer                               21.265181
DroughtTrtExt (90):siteIDTjøtta                                  24.167462
ageClassPioneer:siteIDTjøtta                                     20.985223
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)   691.038720
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer      690.949661
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta         691.855186
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer 722.934568
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta    742.953442
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta       741.608596
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                690.550628
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                   690.989197
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                      691.341728
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  16.811103
                                                                t value
(Intercept)                                                      17.223
speciesVaccinium vitis-idaea                                      4.754
leaf_ageyoung                                                    -4.857
DroughtTrtExt (90)                                               -2.050
ageClassPioneer                                                  -1.115
siteIDTjøtta                                                      0.512
speciesVaccinium vitis-idaea:leaf_ageyoung                       -0.230
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                   2.494
speciesVaccinium vitis-idaea:ageClassPioneer                      1.749
speciesVaccinium vitis-idaea:siteIDTjøtta                         0.309
leaf_ageyoung:DroughtTrtExt (90)                                  1.196
leaf_ageyoung:ageClassPioneer                                    -1.067
leaf_ageyoung:siteIDTjøtta                                       -2.459
DroughtTrtExt (90):ageClassPioneer                                1.085
DroughtTrtExt (90):siteIDTjøtta                                   1.404
ageClassPioneer:siteIDTjøtta                                      0.678
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)    -0.848
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer       -0.842
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta           2.635
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer  -0.231
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta     -2.491
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta        -1.225
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                  0.191
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                    -0.131
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                        1.594
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  -1.024
                                                                Pr(>|t|)    
(Intercept)                                                      < 2e-16 ***
speciesVaccinium vitis-idaea                                    2.41e-06 ***
leaf_ageyoung                                                   1.48e-06 ***
DroughtTrtExt (90)                                               0.04816 *  
ageClassPioneer                                                  0.27555    
siteIDTjøtta                                                     0.61291    
speciesVaccinium vitis-idaea:leaf_ageyoung                       0.81799    
speciesVaccinium vitis-idaea:DroughtTrtExt (90)                  0.01286 *  
speciesVaccinium vitis-idaea:ageClassPioneer                     0.08070 .  
speciesVaccinium vitis-idaea:siteIDTjøtta                        0.75744    
leaf_ageyoung:DroughtTrtExt (90)                                 0.23213    
leaf_ageyoung:ageClassPioneer                                    0.28631    
leaf_ageyoung:siteIDTjøtta                                       0.01418 *  
DroughtTrtExt (90):ageClassPioneer                               0.29022    
DroughtTrtExt (90):siteIDTjøtta                                  0.17301    
ageClassPioneer:siteIDTjøtta                                     0.50507    
speciesVaccinium vitis-idaea:leaf_ageyoung:DroughtTrtExt (90)    0.39653    
speciesVaccinium vitis-idaea:leaf_ageyoung:ageClassPioneer       0.40025    
speciesVaccinium vitis-idaea:leaf_ageyoung:siteIDTjøtta          0.00861 ** 
speciesVaccinium vitis-idaea:DroughtTrtExt (90):ageClassPioneer  0.81706    
speciesVaccinium vitis-idaea:DroughtTrtExt (90):siteIDTjøtta     0.01294 *  
speciesVaccinium vitis-idaea:ageClassPioneer:siteIDTjøtta        0.22104    
leaf_ageyoung:DroughtTrtExt (90):ageClassPioneer                 0.84885    
leaf_ageyoung:DroughtTrtExt (90):siteIDTjøtta                    0.89597    
leaf_ageyoung:ageClassPioneer:siteIDTjøtta                       0.11136    
DroughtTrtExt (90):ageClassPioneer:siteIDTjøtta                  0.32023    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation matrix not shown by default, as p = 26 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
performance::check_model(thickness_three_way_interactions, detrend = FALSE)

Calluna shoot type (Long and Short) only southern site had SS and LS leaves

#create a data frame for calluna lygra site
calluna_data <- droughtnet %>%
  filter(species == "Calluna vulgaris" & siteID == "Lygra")
view(subset_data)
# Create a data frame for Calluna vulgaris at the Lygra site and remove rows with NA values
calluna_shoot <- droughtnet_data2_clean %>%
  filter(species == "Calluna vulgaris" & siteID == "Lygra") %>%
  drop_na()

view(calluna_shoot)

SLA

#calluna shoot type * drought treatment
shoot_type_sla1 <- lmer(log(SLA) ~ calluna_shoot_type +
                               (1 | DroughNet_plotID/plant_nr), 
                             data = calluna_shoot)
summary(shoot_type_sla1)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ calluna_shoot_type + (1 | DroughNet_plotID/plant_nr)
   Data: calluna_shoot

REML criterion at convergence: -184.3

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.6848 -0.5395  0.1254  0.6447  2.2287 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.013066 0.11430 
 DroughNet_plotID          (Intercept) 0.001308 0.03616 
 Residual                              0.015593 0.12487 
Number of obs: 195, groups:  
plant_nr:DroughNet_plotID, 36; DroughNet_plotID, 12

Fixed effects:
                         Estimate Std. Error        df t value Pr(>|t|)    
(Intercept)               4.34701    0.02537  14.71672 171.354   <2e-16 ***
calluna_shoot_typeShort  -0.04379    0.01816 160.95661  -2.411    0.017 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr)
clln_sht_tS -0.373
performance::check_model(shoot_type_sla1, detrend = FALSE)

#calluna shoot type
shoot_type_sla2 <- lmer(log(SLA) ~ (calluna_shoot_type + DroughtTrt + ageClass)^2 +
                               (1 | DroughNet_plotID), 
                             data = calluna_shoot)
summary(shoot_type_sla2)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ (calluna_shoot_type + DroughtTrt + ageClass)^2 + (1 |  
    DroughNet_plotID)
   Data: calluna_shoot

REML criterion at convergence: -123.4

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.7819 -0.5808 -0.0653  0.5747  3.5990 

Random effects:
 Groups           Name        Variance Std.Dev.
 DroughNet_plotID (Intercept) 0.004246 0.06516 
 Residual                     0.025218 0.15880 
Number of obs: 195, groups:  DroughNet_plotID, 12

Fixed effects:
                                             Estimate Std. Error         df
(Intercept)                                  4.409829   0.050096  13.229583
calluna_shoot_typeShort                     -0.039161   0.040711 181.971790
DroughtTrtExt (90)                          -0.027967   0.067370  10.915467
ageClassPioneer                             -0.114794   0.067101  10.737601
calluna_shoot_typeShort:DroughtTrtExt (90)  -0.003246   0.045758 180.847441
calluna_shoot_typeShort:ageClassPioneer     -0.009238   0.045777 180.862011
DroughtTrtExt (90):ageClassPioneer           0.043612   0.088045   7.992887
                                           t value Pr(>|t|)    
(Intercept)                                 88.027   <2e-16 ***
calluna_shoot_typeShort                     -0.962    0.337    
DroughtTrtExt (90)                          -0.415    0.686    
ageClassPioneer                             -1.711    0.116    
calluna_shoot_typeShort:DroughtTrtExt (90)  -0.071    0.944    
calluna_shoot_typeShort:ageClassPioneer     -0.202    0.840    
DroughtTrtExt (90):ageClassPioneer           0.495    0.634    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) cll__S DrTE(90) agClsP c__S:( c__S:C
clln_sht_tS -0.464                                     
DrghtTE(90) -0.693  0.237                              
ageClassPnr -0.700  0.246  0.453                       
c__S:DTE(90  0.271 -0.583 -0.372   -0.030              
clln_s_S:CP  0.274 -0.589 -0.019   -0.364  0.004       
DrTE(90):CP  0.462 -0.034 -0.671   -0.667  0.032  0.016
performance::check_model(shoot_type_sla2, detrend = FALSE)

#calluna shoot type
shoot_type_sla3 <- lmer(log(SLA) ~ (calluna_shoot_type * DroughtTrt * ageClass) +
                               (1 | DroughNet_plotID), 
                             data = calluna_shoot)
summary(shoot_type_sla3)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: log(SLA) ~ (calluna_shoot_type * DroughtTrt * ageClass) + (1 |  
    DroughNet_plotID)
   Data: calluna_shoot

REML criterion at convergence: -120.5

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.7913 -0.5953 -0.0770  0.5889  3.5730 

Random effects:
 Groups           Name        Variance Std.Dev.
 DroughNet_plotID (Intercept) 0.004251 0.0652  
 Residual                     0.025349 0.1592  
Number of obs: 195, groups:  DroughNet_plotID, 12

Fixed effects:
                                                            Estimate Std. Error
(Intercept)                                                  4.40678    0.05214
calluna_shoot_typeShort                                     -0.03382    0.04780
DroughtTrtExt (90)                                          -0.02233    0.07238
ageClassPioneer                                             -0.10935    0.07180
calluna_shoot_typeShort:DroughtTrtExt (90)                  -0.01355    0.06638
calluna_shoot_typeShort:ageClassPioneer                     -0.01945    0.06603
DroughtTrtExt (90):ageClassPioneer                           0.03339    0.10015
calluna_shoot_typeShort:DroughtTrtExt (90):ageClassPioneer   0.01975    0.09185
                                                                  df t value
(Intercept)                                                 15.33492  84.514
calluna_shoot_typeShort                                    181.55952  -0.707
DroughtTrtExt (90)                                          14.35926  -0.309
ageClassPioneer                                             13.89861  -1.523
calluna_shoot_typeShort:DroughtTrtExt (90)                 180.52816  -0.204
calluna_shoot_typeShort:ageClassPioneer                    180.53640  -0.295
DroughtTrtExt (90):ageClassPioneer                          13.22300   0.333
calluna_shoot_typeShort:DroughtTrtExt (90):ageClassPioneer 179.90609   0.215
                                                           Pr(>|t|)    
(Intercept)                                                  <2e-16 ***
calluna_shoot_typeShort                                       0.480    
DroughtTrtExt (90)                                            0.762    
ageClassPioneer                                               0.150    
calluna_shoot_typeShort:DroughtTrtExt (90)                    0.838    
calluna_shoot_typeShort:ageClassPioneer                       0.769    
DroughtTrtExt (90):ageClassPioneer                            0.744    
calluna_shoot_typeShort:DroughtTrtExt (90):ageClassPioneer    0.830    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
              (Intr) cll__S DrTE(90) agClsP cl__S:DTE(90) c__S:C DTE(90):
clln_sht_tS   -0.524                                                     
DrghtTE(90)   -0.720  0.377                                              
ageClassPnr   -0.726  0.380  0.523                                       
cl__S:DTE(90)  0.377 -0.720 -0.502   -0.274                              
clln_s_S:CP    0.379 -0.724 -0.273   -0.490  0.521                       
DrTE(90):CP    0.521 -0.273 -0.723   -0.717  0.363         0.351         
c__S:DTE(90): -0.273  0.520  0.363    0.352 -0.723        -0.719 -0.475  
performance::check_model(shoot_type_sla3, detrend = FALSE)

LMDC

shoot_type1 <- lmer(LDMC ~ calluna_shoot_type +
                               (1 | DroughNet_plotID), 
                             data = calluna_shoot)
summary(shoot_type1)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: LDMC ~ calluna_shoot_type + (1 | DroughNet_plotID)
   Data: calluna_shoot

REML criterion at convergence: 1950.5

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.9327 -0.5647  0.0906  0.6132  2.4790 

Random effects:
 Groups           Name        Variance Std.Dev.
 DroughNet_plotID (Intercept)  303.1   17.41   
 Residual                     1249.0   35.34   
Number of obs: 195, groups:  DroughNet_plotID, 12

Fixed effects:
                        Estimate Std. Error      df t value Pr(>|t|)    
(Intercept)              361.934      6.212  16.385  58.268   <2e-16 ***
calluna_shoot_typeShort    3.020      5.088 183.102   0.594    0.554    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr)
clln_sht_tS -0.422
performance::check_model(shoot_type1, detrend = FALSE)

shoot_type_lmdc2 <- lmer(LDMC ~ (calluna_shoot_type + DroughtTrt + ageClass)^2 +
                               (1 | DroughNet_plotID), 
                             data = calluna_shoot)
summary(shoot_type_lmdc2)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: LDMC ~ (calluna_shoot_type + DroughtTrt + ageClass)^2 + (1 |  
    DroughNet_plotID)
   Data: calluna_shoot

REML criterion at convergence: 1901

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.9088 -0.4526  0.1027  0.6127  2.4731 

Random effects:
 Groups           Name        Variance Std.Dev.
 DroughNet_plotID (Intercept)  210.3   14.50   
 Residual                     1196.1   34.59   
Number of obs: 195, groups:  DroughNet_plotID, 12

Fixed effects:
                                           Estimate Std. Error       df t value
(Intercept)                                358.5181    11.0468  13.2658  32.454
calluna_shoot_typeShort                    -13.4980     8.8673 182.0191  -1.522
DroughtTrtExt (90)                          16.1056    14.8745  10.9969   1.083
ageClassPioneer                            -14.4676    14.8167  10.8230  -0.976
calluna_shoot_typeShort:DroughtTrtExt (90)   0.6182     9.9660 180.9414   0.062
calluna_shoot_typeShort:ageClassPioneer     31.4720     9.9703 180.9554   3.157
DroughtTrtExt (90):ageClassPioneer          12.8525    19.4838   8.1264   0.660
                                           Pr(>|t|)    
(Intercept)                                4.98e-14 ***
calluna_shoot_typeShort                     0.12969    
DroughtTrtExt (90)                          0.30208    
ageClassPioneer                             0.35017    
calluna_shoot_typeShort:DroughtTrtExt (90)  0.95060    
calluna_shoot_typeShort:ageClassPioneer     0.00187 ** 
DroughtTrtExt (90):ageClassPioneer          0.52773    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) cll__S DrTE(90) agClsP c__S:( c__S:C
clln_sht_tS -0.459                                     
DrghtTE(90) -0.694  0.234                              
ageClassPnr -0.700  0.243  0.455                       
c__S:DTE(90  0.267 -0.583 -0.367   -0.029              
clln_s_S:CP  0.270 -0.589 -0.019   -0.359  0.004       
DrTE(90):CP  0.463 -0.033 -0.672   -0.668  0.031  0.016
performance::check_model(shoot_type_lmdc2, detrend = FALSE)

#calluna shoot type
shoot_type_lmdc3 <- lmer(LDMC ~ (calluna_shoot_type * DroughtTrt * ageClass) +
                               (1 | DroughNet_plotID/plant_nr), 
                             data = calluna_shoot)
summary(shoot_type_lmdc3)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: 
LDMC ~ (calluna_shoot_type * DroughtTrt * ageClass) + (1 | DroughNet_plotID/plant_nr)
   Data: calluna_shoot

REML criterion at convergence: 1851.2

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.2601 -0.5085  0.0443  0.6453  2.4919 

Random effects:
 Groups                    Name        Variance Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 609.66   24.69   
 DroughNet_plotID          (Intercept)  56.55    7.52   
 Residual                              758.85   27.55   
Number of obs: 195, groups:  
plant_nr:DroughNet_plotID, 36; DroughNet_plotID, 12

Fixed effects:
                                                           Estimate Std. Error
(Intercept)                                                 357.591     11.333
calluna_shoot_typeShort                                     -13.137      8.466
DroughtTrtExt (90)                                           18.262     15.783
ageClassPioneer                                             -15.413     15.697
calluna_shoot_typeShort:DroughtTrtExt (90)                   -1.199     11.699
calluna_shoot_typeShort:ageClassPioneer                      31.795     11.591
DroughtTrtExt (90):ageClassPioneer                           12.228     21.949
calluna_shoot_typeShort:DroughtTrtExt (90):ageClassPioneer    2.492     16.071
                                                                df t value
(Intercept)                                                 12.529  31.552
calluna_shoot_typeShort                                    160.797  -1.552
DroughtTrtExt (90)                                          11.838   1.157
ageClassPioneer                                             11.578  -0.982
calluna_shoot_typeShort:DroughtTrtExt (90)                 159.123  -0.102
calluna_shoot_typeShort:ageClassPioneer                    158.538   2.743
DroughtTrtExt (90):ageClassPioneer                          11.096   0.557
calluna_shoot_typeShort:DroughtTrtExt (90):ageClassPioneer 157.473   0.155
                                                           Pr(>|t|)    
(Intercept)                                                2.56e-13 ***
calluna_shoot_typeShort                                     0.12269    
DroughtTrtExt (90)                                          0.27006    
ageClassPioneer                                             0.34621    
calluna_shoot_typeShort:DroughtTrtExt (90)                  0.91852    
calluna_shoot_typeShort:ageClassPioneer                     0.00679 ** 
DroughtTrtExt (90):ageClassPioneer                          0.58852    
calluna_shoot_typeShort:DroughtTrtExt (90):ageClassPioneer  0.87699    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
              (Intr) cll__S DrTE(90) agClsP cl__S:DTE(90) c__S:C DTE(90):
clln_sht_tS   -0.437                                                     
DrghtTE(90)   -0.718  0.314                                              
ageClassPnr   -0.722  0.315  0.518                                       
cl__S:DTE(90)  0.316 -0.724 -0.413   -0.228                              
clln_s_S:CP    0.319 -0.730 -0.229   -0.401  0.529                       
DrTE(90):CP    0.516 -0.226 -0.719   -0.715  0.297         0.287         
c__S:DTE(90): -0.230  0.527  0.300    0.289 -0.728        -0.721 -0.384  
performance::check_model(shoot_type_lmdc3, detrend = FALSE)

Thickness

shoot_type_thickness1 <- lmer(mean_thickness ~ calluna_shoot_type +
                               (1 | DroughNet_plotID), 
                             data = calluna_shoot)
summary(shoot_type_thickness1)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ calluna_shoot_type + (1 | DroughNet_plotID)
   Data: calluna_shoot

REML criterion at convergence: -577.6

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.3436 -0.5866 -0.1507  0.5192  3.8789 

Random effects:
 Groups           Name        Variance  Std.Dev.
 DroughNet_plotID (Intercept) 0.0004753 0.02180 
 Residual                     0.0025878 0.05087 
Number of obs: 195, groups:  DroughNet_plotID, 12

Fixed effects:
                         Estimate Std. Error        df t value Pr(>|t|)    
(Intercept)             2.686e-01  8.197e-03 1.726e+01  32.774  < 2e-16 ***
calluna_shoot_typeShort 5.495e-02  7.321e-03 1.830e+02   7.506 2.57e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr)
clln_sht_tS -0.460
performance::check_model(shoot_type_thickness1, detrend = FALSE)

shoot_type_thickness2 <- lmer(mean_thickness ~ (calluna_shoot_type + DroughtTrt + ageClass)^2 +
                               (1 | DroughNet_plotID), 
                             data = calluna_shoot)
boundary (singular) fit: see help('isSingular')
summary(shoot_type_thickness2)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ (calluna_shoot_type + DroughtTrt + ageClass)^2 +  
    (1 | DroughNet_plotID)
   Data: calluna_shoot

REML criterion at convergence: -565.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.2123 -0.6339 -0.1246  0.5776  3.8954 

Random effects:
 Groups           Name        Variance Std.Dev.
 DroughNet_plotID (Intercept) 0.000000 0.00000 
 Residual                     0.002545 0.05044 
Number of obs: 195, groups:  DroughNet_plotID, 12

Fixed effects:
                                             Estimate Std. Error         df
(Intercept)                                  0.239041   0.010392 188.000000
calluna_shoot_typeShort                      0.053890   0.012841 188.000000
DroughtTrtExt (90)                           0.012417   0.013062 188.000000
ageClassPioneer                              0.062060   0.012911 188.000000
calluna_shoot_typeShort:DroughtTrtExt (90)   0.007819   0.014492 188.000000
calluna_shoot_typeShort:ageClassPioneer     -0.004373   0.014497 188.000000
DroughtTrtExt (90):ageClassPioneer          -0.033099   0.014496 188.000000
                                           t value Pr(>|t|)    
(Intercept)                                 23.002  < 2e-16 ***
calluna_shoot_typeShort                      4.197 4.17e-05 ***
DroughtTrtExt (90)                           0.951   0.3430    
ageClassPioneer                              4.807 3.13e-06 ***
calluna_shoot_typeShort:DroughtTrtExt (90)   0.540   0.5902    
calluna_shoot_typeShort:ageClassPioneer     -0.302   0.7632    
DroughtTrtExt (90):ageClassPioneer          -2.283   0.0235 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) cll__S DrTE(90) agClsP c__S:( c__S:C
clln_sht_tS -0.698                                     
DrghtTE(90) -0.672  0.379                              
ageClassPnr -0.690  0.398  0.371                       
c__S:DTE(90  0.406 -0.581 -0.603   -0.044              
clln_s_S:CP  0.410 -0.587 -0.026   -0.594  0.000       
DrTE(90):CP  0.409 -0.060 -0.608   -0.593  0.058  0.027
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')
performance::check_model(shoot_type_thickness2, detrend = FALSE)

shoot_type_thickness3 <- lmer(mean_thickness ~ (calluna_shoot_type * DroughtTrt * ageClass) +
                               (1 | DroughNet_plotID/plant_nr), 
                             data = calluna_shoot)
boundary (singular) fit: see help('isSingular')
summary(shoot_type_thickness3)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_thickness ~ (calluna_shoot_type * DroughtTrt * ageClass) +  
    (1 | DroughNet_plotID/plant_nr)
   Data: calluna_shoot

REML criterion at convergence: -568.5

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.9497 -0.6137 -0.1651  0.4601  3.7269 

Random effects:
 Groups                    Name        Variance  Std.Dev.
 plant_nr:DroughNet_plotID (Intercept) 0.0004477 0.02116 
 DroughNet_plotID          (Intercept) 0.0000000 0.00000 
 Residual                              0.0021493 0.04636 
Number of obs: 195, groups:  
plant_nr:DroughNet_plotID, 36; DroughNet_plotID, 12

Fixed effects:
                                                             Estimate
(Intercept)                                                  0.239650
calluna_shoot_typeShort                                      0.050998
DroughtTrtExt (90)                                           0.011215
ageClassPioneer                                              0.060160
calluna_shoot_typeShort:DroughtTrtExt (90)                   0.013297
calluna_shoot_typeShort:ageClassPioneer                      0.004369
DroughtTrtExt (90):ageClassPioneer                          -0.028080
calluna_shoot_typeShort:DroughtTrtExt (90):ageClassPioneer  -0.016295
                                                           Std. Error
(Intercept)                                                  0.012781
calluna_shoot_typeShort                                      0.014043
DroughtTrtExt (90)                                           0.017562
ageClassPioneer                                              0.017338
calluna_shoot_typeShort:DroughtTrtExt (90)                   0.019488
calluna_shoot_typeShort:ageClassPioneer                      0.019336
DroughtTrtExt (90):ageClassPioneer                           0.023980
calluna_shoot_typeShort:DroughtTrtExt (90):ageClassPioneer   0.026881
                                                                   df t value
(Intercept)                                                 73.584914  18.751
calluna_shoot_typeShort                                    165.448585   3.632
DroughtTrtExt (90)                                          69.574798   0.639
ageClassPioneer                                             66.619031   3.470
calluna_shoot_typeShort:DroughtTrtExt (90)                 162.212261   0.682
calluna_shoot_typeShort:ageClassPioneer                    160.752230   0.226
DroughtTrtExt (90):ageClassPioneer                          63.480783  -1.171
calluna_shoot_typeShort:DroughtTrtExt (90):ageClassPioneer 158.682618  -0.606
                                                           Pr(>|t|)    
(Intercept)                                                 < 2e-16 ***
calluna_shoot_typeShort                                    0.000375 ***
DroughtTrtExt (90)                                         0.525166    
ageClassPioneer                                            0.000918 ***
calluna_shoot_typeShort:DroughtTrtExt (90)                 0.496022    
calluna_shoot_typeShort:ageClassPioneer                    0.821518    
DroughtTrtExt (90):ageClassPioneer                         0.245976    
calluna_shoot_typeShort:DroughtTrtExt (90):ageClassPioneer 0.545240    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
              (Intr) cll__S DrTE(90) agClsP cl__S:DTE(90) c__S:C DTE(90):
clln_sht_tS   -0.633                                                     
DrghtTE(90)   -0.728  0.461                                              
ageClassPnr   -0.737  0.467  0.536                                       
cl__S:DTE(90)  0.456 -0.721 -0.612   -0.336                              
clln_s_S:CP    0.460 -0.726 -0.335   -0.598  0.523                       
DrTE(90):CP    0.533 -0.337 -0.732   -0.723  0.448         0.433         
c__S:DTE(90): -0.331  0.522  0.443    0.430 -0.725        -0.719 -0.583  
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')
performance::check_model(shoot_type_thickness3, detrend = FALSE)